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эя§ " " ь1= ¦Mд?GЎ эя§ " " nј'X Ѓй? ґ эя§ " " ·џ 3Xб?wµ эя§ " " S#дэщfр?3» A эя§ " " S#дэщfр?4» B эя§ " " B•• юѕо?cї эя§ " ".°Џё8wЩ?qД A эя§ " ".°Џё8wЩ? fake fake longines watche Fake Oakley Г“culos Fake Omega Seamaster Euro ​ENTREGA GRГЃTISpara encomendas superioresВЈ. Z[\]^ `abcd efg hijkll m[anop]^qrhsoc^tb u]avw lkfxy r xykyl z {b|w lkfxy r xyfy}. ]i~​btaw ~b^ct bЂo[~~]^]qq]^vЃ[~. ‚vocs]Ѓ‚a]^Ђo[~~]^]qq]^vЃ[~ ѓ„. Z[\]^ `abcd efg hijkll m[anop]^qrhsoc^tb u]avw lkfxy r xykyl z {b|w lkfxy r xyfy}. ]i~​btaw ~b^ct bЂo[~~]^]qq]^vЃ[~. ‚vocs]Ѓ‚a]^Ђo[~~]^]qq]^vЃ[~ ѓ„. ѕпБ¦ЗТјш ѕшБцёё ЖчЕРАє АЪµїАё·О јТёк µЕ ї©±вј №юѕоіѕЯ µЕ! їмё°Ў АвАёёй µЕ ёрµОё¦ ґЩ ѕч±Ч·№АМµе ЅГДСБЩІІ ґ©±ј ѕч±Ч·№АМµе ЗСґЩ°н? г. Березники kensee.coиковская, 63 (Управление "Кудесник") тел.8 () 12 JГ¤ger gespendet eine fabelhafte mit verknГјpften zwischen ВЈ off Wildfleisch tatsГ¤chlich [url=kensee.co]ugg boots uk[/​url]. ловачко-бомбардерске ескадриле РВ ВЈ који је погинуо током НАТО агресије на СРЈ на борбеном задатку. А это уже современная Сербия (​ г.). Команданти АБХО јединица ВЈ који су били на Космету године Фото Приватна арахива. Open А это уже современная Сербия ( г.). heineken.

Fare molta attenzione: le lame sono taglienti. Queste protezioni vengono usate solo come misura protettiva durante la fabbricazione e il trasporto e possono essere gettate.

Rimuovere la confezione e le etichette. Rimuovere sempre la lama prima di svuotare il recipiente. Prima di versare liquidi nel frullatore farli raffreddare a temperatura ambiente.

Non bagnare il motore, il cavo o la spina. Non lasciar pendere il cavo elettrico dal piano di lavoro e non lasciare che tocchi superfici calde.

Per fermarla in posizione, ruotare in senso orario. Ora inserire il tappo di riempimento. Se la miscelazione risultasse difficoltosa, aggiungere altro liquido.

Spegnere non appena si ottiene la consistenza desiderata. Non introdurre ingredienti secchi nel frullatore prima di accenderlo.

Non usare il frullatore per conservare alimenti. La consistenza ottenuta dipende dal tempo di lavorazione.

Utilizzare la lama per preparare torte e dolci, macinare carne cruda e cotta, vegetali, noci, preparare pasticci, creme, zuppe cremose e sbriciolare biscotti e pane.

Usare la lama per impastare per gli impasti a lievitazione. Per la preparazione delle torte, usare burro appena estratto dal frigorifero e tagliato in cubetti di 2 cm.

Non esagerare con il tempo di lavorazione. Non infilare le dita nel tubo di riempimento. Lavorare per 60 secondi fino a ottenere una palla di impasto omogenea ed elastica.

Reimpastare solo a mano. Accendere e premere il frutto sul cono. Per preparare torte, utilizzare sempre la lama.

Accertarsi che il recipiente e lo sbattitore siano puliti e privi di qualsiasi traccia di burro prima di azionarli. Lato per affettare: affetta formaggio, carote, patate, cavolo, cetrioli, zucchine, barbabietola e cipolle.

Maneggiare le lame e i dischi affilati con cautela in quanto sono estremamente taglienti. Alcuni alimenti possono scolorire la plastica.

Sfregare con un panno imbevuto di olio vegetale per eliminare la macchia. Lavare a mano la caraffa. Rimuovere e lavare la guarnizione.

Non toccare le lame affilate, utilizzare una spugna con acqua insaponata per pulirle e sciacquarle abbondantemente con acqua corrente.

Lavarle in acqua tiepida e sapone. Strofinare la testa di azionamento con un panno umido, quindi asciugare. Si consiglia un ciclo di lavaggio breve e a bassa temperatura.

Retire todas as embalagens e eventuais etiquetas. Manusei-os com cuidado. Utilize sempre o s calcador es fornecido s. Coloque a tampa da zona de enchimento.

Mantenha-o vazio antes e depois de o utilizar. Demora cerca de 60 segs. Em seguida, ligue o aparelho e pressione a fruta contra o cone.

Isto evita que os alimentos deslizem para o lado durante o processamento. Os alimentos colocados na vertical saem mais curtos do que os colocados na horizontal.

Recomendamos um programa de lavagem curto a baixa temperatura. Quite todo el embalaje y las etiquetas. Sostenga siempre la cuchilla por el asa, situada en la parte superior, y mantenga los dedos alejados de los bordes cortantes, tanto durante el uso como en las operaciones de limpieza.

Retire siempre la cuchilla antes de vaciar el contenido del bol. Utilice siempre el embutidor que se suministra con el aparato.

Nunca utilice un accesorio no autorizado. Nunca deje este aparato desatendido. Nunca permita que se mojen el bloque motor, el cable o el enchufe.

No ponga ingredientes secos en la licuadora antes de ponerla en marcha. Para masas con levadura utilice la herramienta para amasar.

Tenga cuidado de no exceder el tiempo de proceso. El reamasado o la forma deben hacerse a mano solamente.

Utilice siempre la cuchilla para hacer tartas. Encienda el aparato y presione la fruta sobre el cono. Utilice el lado del rebanador para cortar quesos, zanahorias, patatas, coles, pepinos, calabacines, remolachas y cebollas.

Llene bien el ancho del tubo de entrada de alimentos. Esto evita que la comida resbale hacia los lados durante el proceso. No retire nunca la tapa hasta que los discos de corte se hayan parado completemante.

Lave la jarra a mano. Retire y lave el anillo sellante. No sumerja la unidad de la cuchilla en el agua. No sumerja el cabezal en agua.

De forma alternativa, pueden lavarse en la bandeja superior del lavavajillas. Se recomienda un programa corto a temperatura suave.

Brug aldrig en defekt maskine. Anvend kun apparatet til husholdningsbrug. Det kan give misfarvning, der ikke kan fjernes. Det er forarbejdningstiden, der bestemmer konsistensen.

Blend ikke krydderier - de kan beskadige plastikdelene. Brug ikke blenderen som opbevaringsboks. Blend aldrig mere end 1. Faste madvarer, f.

Tykke blandinger, f. Tungere blandinger med f. Det er ganske normalt og skader ikke plastikken eller giver afsmag i maden. Misfarvninger kan fjernes ved at gnide dem med en klud dyppet i spiseolie.

Dette forhindrer ingredienserne i at glide ud til siden under blendning. Ingredienser der placeres i lodret position kommer ud i mindre stykker, end ingredienser der placeres i vandret position.

Det anbefales at man anvender et kort program med lav temperatur. Mixa aldrig kryddor - plasten kan skadas. Tjocka blandningar, t.

Ta loss packningsringen och diska den. Diska i varmt vatten. Torka av drivhuvudet med fuktig trasa och torka sedan torrt.

Doppa aldrig ner drivhuvudet i vatten. Fjern all emballasje og eventuelle merkesedler. Bruk kun originalt ekstrautstyr.

Bruk aldri en defekt foodprocessor. Bruk bare apparatet til dets tiltenkte hjemlige bruk. Tries are found in two varieties: abbreviated and full.

The former comprise only the shortest prefixes necessary to distinguish the strings; finding a string in them must be confirmed by a comparison to a suffix stored in a trie leaf.

The latter comprise entire strings, character by character, up to a string delimiter, as shown in Figure 1. Dashed arrows indicate implicit links.

In a plain trie the set of arcs coming from each node is represented as an array of size equal to the alphabet size, whose elements are either pointers to child nodes or null pointers.

This technique needs excessive amounts of storage for large collections of strings. Memory usage decreases at the cost of retrieval time by eliminating null pointers and arranging the remaining pointers into a list or a binary search tree.

Furthermore, static lists and static complete binary trees occupying subsequent memory locations can get along with one bit instead of an explicit link to a successor, as shown in Figure 2.

An alternative approach, which does not compromise the search time, is to overlap the nodes, so that all the non-null pointers retain their positions within a node and occupy empty locations of the other nodes [2].

Path compression generalizes the concept of abbreviated tries: a path-compressed trie replaces single paths with single arcs, using strings for branching.

Still other methods of reducing the trie size, such as C-trie [16] and Bonsai [8], lower the space occupied by a node, ingeniously using only one bit per pointer or one pointer to all the offspring nodes.

Finite automata We concentrate on yet another technique that consists in merging all equivalent subtries of a full trie and can coexist with any method of node packing that preserves distinct pointers to child nodes.

Comparing the trie in Figure 1 with the directed acyclic graph in Figure 3 clears this idea. Intuitively, it is especially attractive when the keys come from a natural language, since they are likely to share many suffixes, and indeed we shall see that such lexicons can be substantially compacted this way.

The obtained structure, which can be viewed as a minimal deterministic finite automaton that recognizes a given set of strings, used to be named directed acyclic word graph DAWG in some publications, but DAWG is actually another concept [4].

From now on we call it a recognizer for short [1, Section 3. Recognizers inherit the advantages of tries, but cannot associate distinct information with the keys, which seems to limit their applications to lexicons.

However, augmenting their states with numeric data provides a minimal perfect hash function of the given strings [15], making recognizers a proper dictionary structure.

This paper discusses static recognizers; dynamic recognizers, which can be updated without rebuilding them from scratch, are dealt by Park et al.

Revuz [22] and Watson [27] have developed incremental algorithms that produce a partially minimized automaton instead of a full trie.

A direct, both space-efficient and fast algorithm to construct a minimal acyclic automaton has been independently invented several times, with secondary differences, by Jan Daciuk [6], Stoyan Mihov [18, 19], Bruce W.

Watson see Reference [7] , and the first author. Simple recognizers To ease the explanation, we begin with what we tentatively call a simple recognizer see Figure 3.

Let us treat transitions as pairs attribute character destination state and states as sets of their out-transitions.

Two transitions are equal if both of their elements are equal. Informally, two states are equivalent if joining them, i. In particular, states with equal sets of outtransitions are equivalent.

As the recognizer is a minimal finite automaton, it contains no equivalent states. There is a distinguished start state, without in-transitions, equivalent to the root of a trie.

As in a full trie, the alphabet of a simple recognizer includes a string delimiter to distinguish the strings that are prefixes of other strings.

Due to the minimality of the automaton, it contains exactly one terminal state. Figure 4 shows the algorithm for constructing a simple recognizer.

The point of the algorithm, first noticed by Mihov [19], lies in such an order of adding states to the recognizer that once a state is formed, it need not be updated.

Therefore, any external representation of the recognizer is supported. The algorithm is sequentially fed with strings. For each prefix of strings in the lexicon, the strings beginning with it shall appear consecutively; otherwise a non-deterministic automaton is constructed instead of a deterministic one.

The most natural way to meet this condition is to sort the strings lexicographically. The presented version fails if the same string occurs more than once, but a trivial modification of line 05, which finds the length of a common prefix of two strings, would immunize it against this case.

Double circles indicate terminal states. Thick arrows indicate terminal transitions. It returns a descriptor of the found or added state, which is an index of its first transition or a pointer to it in a most natural representation of a recognizer.

It turns out that joining equal states at this moment yields a minimized recognizer without any equivalent states.

The algorithm maintains an auxiliary data structure, not mentioned explicitly in Figure 4. Of course, it is not needed for using the recognizer when its construction finishes.

A naive implementation missing the hash table can linearly search the recognizer, achieving quadratic running time. Figure 5 shows the values of the variables in the course of an example construction, between the lines 05 and 06 of the algorithm.

Whereas this function finds in the recognizer a state equal to the given one using its hash table, we have to find it below the dotted line with our eyes.

In the initial two iterations, it is there; in the remaining two iterations, it is not. Other types of recognizers This section treats recognizers with fewer states and transitions than their simple counterparts.

Finite automata with output encoded in their states are called Moore machines [10, Chapter 2. Changing our definition of a state to a pair set of transitions, terminality bit yields a specimen of acyclic Moore machine with one-bit output.

Such a Moore recognizer for the sample set of strings is presented in Figure 6. There are also Mealy machines that have their output encoded in the transitions.

Defining a transition as a triple attribute character destination state terminality bit , equality of transitions as equality of triples, and a state again as a set of transitions, we get a Mealy recognizer see Figure 7.

The only distinction in using them is rather of theoretical interest: Mealy recognizers cannot recognize the empty string, Moore and simple recognizers can.

Direct algorithms creating Moore and Mealy recognizers are presented in Figure 8. One can imagine also dual automata with attribute characters encoded in states instead of transitions, and writing algorithms creating minimal acyclic automata of this kind is an easy exercise.

If, after several attempts, the load is not balanced correctly, the machine spins at a reduced spin speed. If the load is excessively unbalanced, the washing machine performs the distribution process instead of spinning.

To encourage improved load distribution and balance, we recommend small and large garments are mixed in the load.

Precautions and tips This washing machine was designed and constructed in accordance with international safety regulations.

The following information is provided for safety reasons and must therefore be read carefully. Hold the plug and pull.

This could damage the safety lock mechanism designed to prevent accidental opening. GB In the event that it is not possible to open the porthole door due to a powercut, and if you wish to remove the laundry, proceed as follows: 20 1.

Never try to do this alone, because the appliance is very heavy. Old appliances must be collected separately in order to optimise the recovery and recycling of the materials they contain and reduce the impact on human health and the environment.

The crossed out "wheeled bin" symbol on the product reminds you of your obligation, that when you dispose of the appliance it must be separately collected.

Consumers should contact their local authority or retailer for information concerning the correct disposal of their old appliance.

This will limit wear on the hydraulic system inside the washing machine and help to prevent leaks. Cleaning the washing machine The outer parts and rubber components of the appliance can be cleaned using a soft cloth soaked in lukewarm soapy water.

Do not use solvents or abrasives. Cleaning the detergent dispenser drawer Remove the dispenser by raising it and pulling it out see figure.

Wash it under running water; this operation should be repeated frequently. Sometimes, small items such as coins or buttons may fall into the pre-chamber which protects the pump, situated in its bottom part.

Make sure the wash cycle has finished and unplug the appliance. To access the pre-chamber: 1. Checking the water inlet hose Check the inlet hose at least once a year.

If there are any cracks, it should be replaced immediately: during the wash cycles, water pressure is very strong and a cracked hose could easily split open.

The wash cycle does not start. The water tap has not been opened. The washing machine does not take in water the indicator light for the first wash cycle stage flashes rapidly.

The hose is bent. There is no water supply in the house. The pressure is too low. The washing machine continuously takes in and drains water.

If the problem persists even after these checks, turn off the water tap, switch the appliance off and contact the Assistance Service.

If the dwelling is on one of the upper floors of a building, there may be problems relating to water drainage, causing the washing machine to fill with water and drain continuously.

Special anti-draining valves are available in shops and help to avoid this inconvenience. The washing machine does not drain or spin.

The washing machine vibrates a lot during the spin cycle. The washing machine leaks. If the problem persists, contact the Technical Assistance Service.

There is too much foam. GB Always request the assistance of authorised technicians. This information can be found on the data plate applied to the rear of the washing machine, and can also be found on the front of the appliance by opening the door.

Rozpakowanie i wypoziomowanie Rozpakowanie 1. Uruchamianie programu 1. BABY program 8. Jest aktywny ze wszystkimi programami. Super Wash Dzieki zastosowaniu wiekszej ilosci wody w poczatkowej fazie cyklu i wydluzeniu czasu trwania programu, funkcja ta gwarantuje pranie o wysokiej skutecznosci.

Pralka nie pobiera wody szybko pulsuje kontrolka pierwszej fazy prania. Pralka mocno wibruje w fazie wirowania. Z pralki wycieka woda.

Pazite, da cev ni prepognjena ali stisnjena. Pralni stroj namestite na ravna in trda tla. Ne uporabljajte rabljenih cevi.

Med potekom pranja se gumb ne premika. Kako zagnati program pranja 1. Perilo vstavite v pralni stroj in zaprite vratca.

Za izbiro posameznih funkcij: 1. Je aktivna z vsemi pralnimi programi. Svila: uporabite primeren program 10 za pranje svilenega perila.

£ In EUR

Lassen Sie die Antriebseinheit, das Netzkabel oder den Stecker niemals nass werden. Darauf achten, dass die Dichtung richtig sitzt. Die Messerscheibe im Uhrzeigersinn festdrehen.

Verwenden Sie den Mixer nicht zum Aufbewahren. Solange er nicht benutzt wird, sollte er leer sein. Mixen Sie niemals mehr als 1.

Die Verarbeitungsdauer bestimmt die erreichte Konsistenz. Verwenden Sie den Teigkneter zur Herstellung von Hefeteigmischungen.

Achten Sie darauf, dass Sie die Zutaten nicht zu lange verarbeiten. Lassen Sie solange kneten, bis sich eine elastische Teigkugel formt.

Dies dauert 60 Sekunden. Kneten Sie noch einmal nur von Hand. Orangen, Zitronen, Limonen und Grapefruits verwendet.

Antriebseinheit Mit einem feuchten Tuch abwischen, dann abtrocknen. Mixkrug Krug ausleeren und von der Messerscheibe losdrehen.

Krug von Hand auswaschen. Entfernen Sie den Dichtungsring und waschen Sie ihn. Tauchen Sie die Klingenhalterung nicht in Wasser.

Waschen Sie sie in warmen Seifenwasser. Wischen Sie den Antriebskopf mit einem feuchten Tuch ab, und trocknen Sie ihn dann.

Tauchen Sie den Antriebskopf nicht in Wasser. Fare molta attenzione: le lame sono taglienti. Queste protezioni vengono usate solo come misura protettiva durante la fabbricazione e il trasporto e possono essere gettate.

Rimuovere la confezione e le etichette. Rimuovere sempre la lama prima di svuotare il recipiente. Prima di versare liquidi nel frullatore farli raffreddare a temperatura ambiente.

Non bagnare il motore, il cavo o la spina. Non lasciar pendere il cavo elettrico dal piano di lavoro e non lasciare che tocchi superfici calde.

Per fermarla in posizione, ruotare in senso orario. Ora inserire il tappo di riempimento. Se la miscelazione risultasse difficoltosa, aggiungere altro liquido.

Spegnere non appena si ottiene la consistenza desiderata. Non introdurre ingredienti secchi nel frullatore prima di accenderlo.

Non usare il frullatore per conservare alimenti. La consistenza ottenuta dipende dal tempo di lavorazione.

Utilizzare la lama per preparare torte e dolci, macinare carne cruda e cotta, vegetali, noci, preparare pasticci, creme, zuppe cremose e sbriciolare biscotti e pane.

Usare la lama per impastare per gli impasti a lievitazione. Per la preparazione delle torte, usare burro appena estratto dal frigorifero e tagliato in cubetti di 2 cm.

Non esagerare con il tempo di lavorazione. Non infilare le dita nel tubo di riempimento. Lavorare per 60 secondi fino a ottenere una palla di impasto omogenea ed elastica.

Reimpastare solo a mano. Accendere e premere il frutto sul cono. Per preparare torte, utilizzare sempre la lama.

Accertarsi che il recipiente e lo sbattitore siano puliti e privi di qualsiasi traccia di burro prima di azionarli. Lato per affettare: affetta formaggio, carote, patate, cavolo, cetrioli, zucchine, barbabietola e cipolle.

Maneggiare le lame e i dischi affilati con cautela in quanto sono estremamente taglienti. Alcuni alimenti possono scolorire la plastica.

Sfregare con un panno imbevuto di olio vegetale per eliminare la macchia. Lavare a mano la caraffa. Rimuovere e lavare la guarnizione.

Non toccare le lame affilate, utilizzare una spugna con acqua insaponata per pulirle e sciacquarle abbondantemente con acqua corrente.

Lavarle in acqua tiepida e sapone. Strofinare la testa di azionamento con un panno umido, quindi asciugare. Si consiglia un ciclo di lavaggio breve e a bassa temperatura.

Retire todas as embalagens e eventuais etiquetas. Manusei-os com cuidado. Utilize sempre o s calcador es fornecido s.

Coloque a tampa da zona de enchimento. Mantenha-o vazio antes e depois de o utilizar. Demora cerca de 60 segs.

Em seguida, ligue o aparelho e pressione a fruta contra o cone. Isto evita que os alimentos deslizem para o lado durante o processamento.

Os alimentos colocados na vertical saem mais curtos do que os colocados na horizontal. Recomendamos um programa de lavagem curto a baixa temperatura.

Quite todo el embalaje y las etiquetas. Sostenga siempre la cuchilla por el asa, situada en la parte superior, y mantenga los dedos alejados de los bordes cortantes, tanto durante el uso como en las operaciones de limpieza.

Retire siempre la cuchilla antes de vaciar el contenido del bol. Utilice siempre el embutidor que se suministra con el aparato.

Nunca utilice un accesorio no autorizado. Nunca deje este aparato desatendido. Nunca permita que se mojen el bloque motor, el cable o el enchufe.

No ponga ingredientes secos en la licuadora antes de ponerla en marcha. Para masas con levadura utilice la herramienta para amasar.

Tenga cuidado de no exceder el tiempo de proceso. El reamasado o la forma deben hacerse a mano solamente. Utilice siempre la cuchilla para hacer tartas.

Encienda el aparato y presione la fruta sobre el cono. Utilice el lado del rebanador para cortar quesos, zanahorias, patatas, coles, pepinos, calabacines, remolachas y cebollas.

Llene bien el ancho del tubo de entrada de alimentos. Esto evita que la comida resbale hacia los lados durante el proceso. No retire nunca la tapa hasta que los discos de corte se hayan parado completemante.

Lave la jarra a mano. Retire y lave el anillo sellante. No sumerja la unidad de la cuchilla en el agua. No sumerja el cabezal en agua.

De forma alternativa, pueden lavarse en la bandeja superior del lavavajillas. Se recomienda un programa corto a temperatura suave.

Brug aldrig en defekt maskine. Anvend kun apparatet til husholdningsbrug. Det kan give misfarvning, der ikke kan fjernes.

Det er forarbejdningstiden, der bestemmer konsistensen. Blend ikke krydderier - de kan beskadige plastikdelene. Brug ikke blenderen som opbevaringsboks.

Blend aldrig mere end 1. Faste madvarer, f. Tykke blandinger, f. Tungere blandinger med f. Det er ganske normalt og skader ikke plastikken eller giver afsmag i maden.

Misfarvninger kan fjernes ved at gnide dem med en klud dyppet i spiseolie. Dette forhindrer ingredienserne i at glide ud til siden under blendning.

Ingredienser der placeres i lodret position kommer ud i mindre stykker, end ingredienser der placeres i vandret position. Det anbefales at man anvender et kort program med lav temperatur.

Mixa aldrig kryddor - plasten kan skadas. Tjocka blandningar, t. Ta loss packningsringen och diska den. Diska i varmt vatten. Torka av drivhuvudet med fuktig trasa och torka sedan torrt.

Doppa aldrig ner drivhuvudet i vatten. Fjern all emballasje og eventuelle merkesedler. Bruk kun originalt ekstrautstyr.

Bruk aldri en defekt foodprocessor. Bruk bare apparatet til dets tiltenkte hjemlige bruk. Kast beskytterne. Ingrediensenes konsistens avhenger av hvor lenge de bearbeides i maskinen.

Hvis du bruker hurtigmikseren i mer enn ett minutt om gangen, vil maskinens levetid forkortes. Ha ikke krydder i hurtigmikseren, da dette kan skade plastmaterialet.

Hurtigmikseren egner seg ikke til oppbevaring. Ha aldri mer enn 1. Skyv begge vispene godt inn i drivhodene i vispinnsatsen.

Tre vispen forsiktig nedover drivakselen. Ha i ingrediensene. Ta ut og vask gummiringen. Legg ikke knivenheten i vann. Dette er helt normalt og skader ikke plasten.

Fjern misfarging med en klut fuktet i vegetabilsk olje. Det hindrer at maten glir sideveis mens den mikses. Vi anbefaler et kort program med lav temperatur.

Poista pakkauksen osat ja mahdolliset tarrat. Valvo aina laitteen toimintaa. Jos tiiviste on vaurioitunut tai huonosti paikoillaan, laite vuotaa.

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Finite automata with output encoded in their states are called Moore machines [10, Chapter 2. Changing our definition of a state to a pair set of transitions, terminality bit yields a specimen of acyclic Moore machine with one-bit output.

Such a Moore recognizer for the sample set of strings is presented in Figure 6. There are also Mealy machines that have their output encoded in the transitions.

Defining a transition as a triple attribute character destination state terminality bit , equality of transitions as equality of triples, and a state again as a set of transitions, we get a Mealy recognizer see Figure 7.

The only distinction in using them is rather of theoretical interest: Mealy recognizers cannot recognize the empty string, Moore and simple recognizers can.

Direct algorithms creating Moore and Mealy recognizers are presented in Figure 8. One can imagine also dual automata with attribute characters encoded in states instead of transitions, and writing algorithms creating minimal acyclic automata of this kind is an easy exercise.

However, using such automata requires twice as many memory reads as using conventional ones, and, moreover, they have in general more states and transitions.

We experimented also with automata that have distinct start states for strings of different length and thus need no explicit terminal states.

Curiously, neither has a minimal recognizer of this type to be unique and acyclic, nor does the presented algorithm guarantee a minimal construction.

Anyhow, the acyclic instances obtained with the direct algorithm have many more states and transitions than ordinary automata. As a final remark for this section, we note that the presented algorithms can be easily modified to handle several types of string delimiters or several bits of terminality.

For example, consider a spelling checker for any language written with an alphabet that distinguishes the case of letters. Although all the words can be stored in a recognizer as they are usually written, it is wiser to convert them to one case and let the terminal state or transition determine the canonical spelling of a word the irregularities being a class on their own with a mask of capitals attached.

This way the recognizer needs to be consulted exactly once for each word checked, regardless of its nontypical capitalization, e.

Also, as a rule it contains slightly fewer states and transitions than a recognizer with a potpourri of lowercase and uppercase characters.

Another application of recognizers for more than one class of strings is discussed in the next section. Comparison of the representations The three types of automata presented above differ in size.

This lexicon comprises the leaves of the directory tree, i. In a search engine, reversed pathnames would be more useful, so we include also results for them.

Their length is uniformly distributed between 4 and 15 characters; each character is independently chosen from a character alphabet.

Table 1 contains some relevant parameters of the lexicons listed above, and Table 2 shows the number of states and transitions in the recognizers constructed for them.

As was expected, the Mealy recognizers are superior to the others in this view. On the other hand, the virtue of simple recognizers is their clean structure.

They can prove useful when a few dozen types of strings exist, i. Their sample application are lexicons that comprise word bases for the morphological analysis of text.

Classes of affixes allowed for a base are encoded in terminal states or transitions of an automaton. Words with the same base can take different affixes, as shown by Latin secur-[us,a,um,.

In these circumstances maintaining a simple recognizer is less cumbersome. The reader, however, should not become convinced that acyclic automata, which are the subject of this paper, are a panacea for natural language processing.

For an account of using automata with cycles to store the potentially infinite lexicons of agglutinative languages, see e.

Reference [20]. The implementation of the other varieties can be easily deduced from it. The recognizer is stored in an array, whose consecutive subarrays represent the out-transitions of recognizer states.

For storing the reversed pathnames, the index field is 30 bits long, making the transitions occupy five bytes each.

The element at index zero represents the state that has no out-transitions, but must occupy space, lest the next state should be mistaken for it.

This otherwise unused location is a convenient place to store the index of the start state. Memory for these records is allocated in large chunks to decrease the time and space overhead of library allocation routines.

On a typical bit machine, the hash table occupies one megabyte for the list heads plus a megabyte for each roughly 87 thousand states.

The average speed of successful lookups, measured by searching all the strings in a lexicon, is between 2 and 4 megabytes per second when the transitions of each state are alphabetically ordered.

Another way to accelerate searching is to sort the transitions of each state with decreasing frequency of use [26].

It can be done with a training collection of strings, assuming that it is typical for future searches.

Recognizing the training strings and counting how many times each transition is taken allows to reorganize the order of transitions in each state.

A binary recognizer that branches on bits of the ASCII code or a static Huffman code of the strings is several times bigger than a recognizer with a character alphabet.

Conversely, the way to reduce the size of recognizers, at least for some lexicons, is to substitute single symbols for frequent groups of characters.

It is however obscure which groups should be replaced. Among several heuristics tried by us, no method to determine feasible substitutions produces consistent results for different lexicons.

For other lexicons, though, it proves better to refrain from the replacement or to do it for only a few character pairs. A more general way to save a little memory is to include some states in larger ones if the former are their subsets.

To this end, we distinguish fresh states, whose transitions are alphabetically ordered, and frozen states that have been reordered to contain a smaller state at the end of the transition list.

For our data, frozen states are rare and rather short, so implementing more elaborate methods is not worth the effort. All the transitions of the larval state are examined to find one that hashes to a bucket with the fewest entries.

The fresh states from this bucket that are larger than the larval state are scanned in order of increasing size for the larval transitions all the buckets are not kept sorted all the time, since only a fraction of them is ever searched.

The scan is pretty fast, as the transitions of both fresh and larval states are alphabetically ordered.

If some state contains all the needed transitions, they are moved to its end and considered a fresh state, and the larger state is frozen.

Otherwise, a fresh state is created the usual way. Mealy recognizer using four bytes per transition, without any additional squeezing. Path-compressed trie.

This way multicharacter arcs need not be split at string ends. Arcs labelled with one character occupy four bytes; longer labels consist of a 7-bit length followed by 7-bit characters.

String ends are marked in nodes, too. C-trie, a trie compaction scheme proposed by Maly [16]. Ispell lexicon file. This file, tailored to spell checking, contains a hash table, a list of base words and allowed affixes, and a few kilobytes of other information.

From these structures, the recognizers occupy the least memory for almost all data sets. The exception of random data, where common prefixes and suffixes are rare, shows that they work best for lexicons that 9 exhibit similarities, such as natural languages.

The lookup speed in all the trie-derived data structures is comparable. In Ispell hash tables it is slower and depends more on the properties of a language.

Speed of operation and frugal use of memory distinguish it from universal minimization algorithms applied to acyclic automata.

The algorithm is shown in three variations for automata that mark string ends in different ways.

The automata using terminal transitions occupy the least memory, the automata using string delimiters suit some applications better.

Particular techniques to decrease the size of automata and accelerate searching them are also discussed. A comparison for real-world data sets shows that the automata, while retaining attractive properties of tries, usually occupy several times less memory than alternative data structures.

Acknowledgements We are grateful to Zbigniew J. Czech, Bruce W. Watson, and the anonymous referees for their critical comments on this paper.

Free lexicons that we used for benchmarks are maintained by Geoff Kuenning, Sergei B. The work was partially financed by a State Committee for Scientific Research grant no.

Compilers: Principles, Techniques and Tools. Algorithms for trie compaction. Complete inverted files for efficient text retrieval and analysis.

Perfect hashing. Incremental construction of minimal acyclic finitestate automata. Bonsai: a compact representation of trees.

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