Among various generalizations of an automaton, fuzzy automaton was the most widely used generalization introduced by Wee [13], while establishing model of learning system. Since then it has been used in many applications [1, 7, 10, 11, 12]. Many classes of fuzzy automata were introduced and studied in [8], few well known, are Automata with weights, L-semi-group automata, Lattice automata, Boolean automata, Semiring automata and Field automata etc. Reduction/minimization of fuzzy automaton was one the important issue in [3, 9], several methods and algorithms of reduction were proposed [3, 9]. Homomorphism and covering are two algebraic notions related to reduction of automata [4, 5]. Isomorphism gives an equivalent copy of the fuzzy automaton, while covering gives a copy of a fuzzy automaton having fewer states and equally powerful in computing. The problem of reduction of states, in terms of homomorphism and covering, for a fuzzy finite state machines was completely resolved in [6, 7], while for finite automata, in terms of congruences and homomorphism was discussed in [9]. A class, pushdown automata, of automata was generalized to fuzzy pushdown automata by Bucurescu and Pascu [2] and Xing [14]. Xing introduced non-**deterministic** fuzzy pushdown automata (NFPA) and found that the class of NFPA languages and fuzzy **context**-**free** K-**grammar** languages are equivalent, while Bucurescu and Pascu found that fuzzy pushdown automata accept **context** sensitive languages by setting a threshold and B-fuzzy automata accept **context**-**free** languages.

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Abstract. In this paper, we propose a two fold generic parser. First, it simulates the behavior of multiple parsing automata. Second, it parses strings drawn from either a **context** **free** **grammar**, a regular tree **grammar**, or from both. The proposed parser is based on an approach that defines an extended version of an automaton, called position- parsing automaton (PPA) using concepts from LR and regular tree automata, combined with a newly introduced concept, called state instantiation and transition cloning. It is constructed as a direct mapping from a **grammar**, represented in an expanded list format. However, PPA is a non-**deterministic** automaton with a generic bottom–up parsing behavior. Hence, it is efficiently transformed into a reduced one (RBA). The proposed parser is then constructed to simulate the run of the RBA automaton on input strings derived from a respective **grammar**. Without loss of generality, the proposed parser is used within the framework of pattern matching and code generation. Comparisons with similar and well-known approaches, such as LR and RI, have shown that our parsing algorithm is conceptually simpler and requires less space and states.

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This paper proposed a method of grammatical induction with error correction for **deterministic** **context**-**free** L-system. Given a transmuted string, the method induces L-system **grammar** candidates. As transmutation this paper focuses only on replacement-type. In the method, a set of parameter values is exhaustively searched and if it is located within the tolerable distance from a point determined by the given string, then the parameters are used to form rule candidates. Rule candidates are used to generate a candidate string, and the similarity between a generated string and the given one is calculated, and candidates having the strongest similarities are shown as the output. Our experiments showed the pro- posed method discovered the true L-system **grammar** when the transmutation rate is less than around 20%. In the future we plan to extend the method to cope with other types of transmutations such as deletion-type or insertion-type.

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An Augmented Context Free Grammar for Discourse An Augmented Context Free Grammar for Discourse Abstract This paper presents an augmented context free grammar which describes important features of the[.]

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Grammatical inference is the machine learning domain which aims at studying learnability of formal languages. While many learnability results have been obtained for regular languages (An- gluin, 1987; Carrasco and Oncina, 1994), this class is not sufficient to correctly represent natural languages. The next class of languages to consider is the class of **context**-**free** languages (CFL). Unfortunately, there exists no learnability results for the whole class. This may be explained by the fact that this class relies on syntactic properties instead of intrinsic properties of the language like the notion of residuals for regular languages (Denis et al., 2004). Thus, most of the approaches proposed in the literature are either based on heuristics (Nakamura and Matsumoto, 2005; Langley and Stromsten, 2000) or are theoretically well founded but concern very restricted subclasses of **context**-**free** languages (Eyraud et al., 2007; Yokomori, 2003; Higuera and Oncina, 2002). Some of these approaches are built from the idea of distributional learning, 1 normally attributed to Harris (1954). The basic principle—as we reinterpret it in our work—is to look at the set of contexts that a substring can occur in. The distribution of a substring is the linguistic way of referring to this set of contexts. This idea has formed the basis of many heuristic algorithms for learning **context**- **free** grammars (see Adriaans, 2002 for instance). However, a recent approach by Clark and Eyraud (2007), has presented an accurate formalisation of distributional learning. From this formulation, a provably correct algorithm for **context**-**free** grammatical inference was given in the identification in the limit framework, albeit for a very limited subclass of languages, the substitutable languages. From a more general point of view, the central insight is that it is not necessary to find the non- terminals of the **context**-**free** **grammar** (CFG): it is enough to be able to represent the congruence classes of a sufficiently large set of substrings of the language and to be able to compute how they combine. This result was extended to a PAC-learning result under a number of different assumptions (Clark, 2006) for a larger class of languages, and also to a family of classes of learnable languages (Yoshinaka, 2008).

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Flat splicing **grammar** systems with **context**-**free** or regular rules in the components have been considered in [2]. In fact essentially, alphabetic flat splicing rules are considered in [2], especially in the proofs of the results, although this is not explicitly mentioned. We refer to these as alphabetic flat splicing **context**-**free** or regular **grammar** systems. When the number of components is /, / ≥ 1, we denote the generated corresponding families of languages respectively by & . () and & . (%). We now introduce a variant called an alphabetic flat splicing pure **context**-**free** **grammar** system which has pure **context**-**free** rules in the components. Rewriting is done in parallel in the components but two different components “communicate” by alphabetic flat splicing rules. We now formally define this **grammar** system.

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Deciding satisfiability for a general ILP LAS **context** task is Σ P 2 complete (in the propositional case); however, if there are no negative examples then the complexity is only N P - complete. ILASP tasks with no negative examples tend to run faster in ILASP than equivalent tasks with negative ex- amples, so when it is possible to modify the representation to eliminate negative examples it is often advantageous to do so. When ASGs are stratified, the representation in Def- inition 10 can be modified to use only positive examples. This can be achieved by representing each constraint : - body as the rule vio : - body (where vio is a new atom that in- dicates that at least one constraint has been violated). The positive CDPI examples in LAS(T, d) are then extended to indicate that the unique answer set of the (stratified) pro- gram should not prove vio (which is equivalent to saying that none of the constraints should be violated). The nega- tive examples in LAS(T, d) are represented similarly (again as positive examples), but indicating that the unique answer set of the (stratified) program must contain vio. This means that the unique answer set must violate at least one constraint to cover the example. If each example string has only a poly- nomial number of parse trees then this task is polynomial in size of the ASG learning task 8 . Hence propositional strati- fied BTS is in NP, provided that each example string has a polynomial number of parse trees.

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Generalized Multitext **Grammar** (GMTG) is a syn- chronous **grammar** formalism that is weakly equiv- alent to Linear **Context**-**Free** Rewriting Systems (LCFRS), but retains much of the notational and in- tuitive simplicity of **Context**-**Free** **Grammar** (CFG). GMTG allows both synchronous and independent rewriting. Such flexibility facilitates more perspic- uous modeling of parallel text than what is possible with other synchronous formalisms. This paper in- vestigates the generative capacity of GMTG, proves that each component **grammar** of a GMTG retains its generative power, and proposes a generalization of Chomsky Normal Form, which is necessary for synchronous CKY-style parsing.

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We now prove that reverse-properness does not restrict the space of probability distributions, by means of the construction of a ‘cover’ **grammar** from an input CFG, as reported in Figure 2. This cover CFG has almost the same structure as the PDT resulting from Figure 1. Rules and transitions al- most stand in a one-to-one relation. The only note- worthy difference is between transitions of type (6) and rules of type (12). The right-hand sides of those rules can be ε because the corresponding transitions are **deterministic** if seen from right to left. Now it becomes clear why we needed the components p in stack symbols of the form (p, A, m). Without it, one could obtain an LR state q that does not match the underlying [p; X] in a reversed computation.

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However, for all variation of Petri net controlled grammars, the production rules of a **grammar** are associated only with transitions of a Petri net. Thus, it is also interesting to consider the place labelling strategies with Petri net controlled grammars. Theoretically, it would complete the node labelling cases, i.e., we study the cases where the production rules are associated with places of a Petri net, not only with its transitions. Moreover, the place labelling makes possible the consideration of parallel application of production rules in Petri net controlled grammars, which allows formal language based models to be developed for synchronized/parallel discrete event systems.

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Each Myanmar consonant has default vowel sound and itself works as a syllable. The set of consonants in Unicode chart is C={က, ခ, ဂ, ဃ, င, စ, ဆ, ဇ, ဈ, ဉ , ည ,ဋ ,ဌ, ဍ, ဎ, ဏ, တ, ထ ,ဒ ,ဓ ,န ,ပ ,ဖ, ဗ, ဘ ,မ ,ယ ,ရ, လ, ၀, သ, ဟ, ဠ } having 33 elements. But, the letter အ can act as consonant as well as **free** standing vowel. Medials or consonant conjuncts mean the modifiers of the syllables` vowel and they are encoded separately in the Unicode encoding. There are four basic medials in Unicode chart and it is represented as the set M={ , , }.

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A 2D **grammar** model [5], which we call here as two-dimensional tabled **context**-**free** **grammar** 2T CF G (originally called tabled **context**- **free** matrix **grammar** in [5]) has been extensively investigated. There are two phases of derivation in a 2T CF G. In the ﬁrst phase hor- izontal strings of symbols are generated using **context**-**free** string **grammar** rules starting from a start symbol. In the second phase, the symbols in these words are in parallel rewritten in the verti- cal direction using right-linear rules which are either of the form A → aB or A → B or A → a or A → λ. But at a step all the rules applied are one of these forms. The family of picture languages generated by 2T CF Gs is denoted by 2T CF L. We now show that the family (l/u)E2DCF P L contains picture languages that cannot be generated by any 2T CF G.

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representation which maintains these beneficial proper- ties. Although proofs have not been provided here, the algorithm can be shown to satisfy our initial formal def- inition of transfer as nondeterministic, exhaustive, non- overlapping replacement of description elements in the source structure by their counterparts as specified in the rewriting rules. The method described in this paper bears some obvious analogy to the classical problem of map- ping a **context**-**free** language into another **context**-**free** language by way of a finite-state transducer (Harrison, 1978). It would be an interesting research question to make this analogy formal, the main difference here be- ing the need to work with a commutative concatenation, as opposed to the standard non-commutative concatena- tion which is more directly connected with the automaton view of transductions.

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between nominative and accusative case is due to the fact that both cases are expressed by identical morphology in the feminine and neutral genders in German. The morphologic similarity between ac- cusative and dative is less substantial, but especially proper names and bare nouns are still subject to con- fusion. As the evaluation results show, the distinc- tion between the cases could be learned in general, but morphological similarity and in addition the rel- atively **free** word order in German impose high de- mands on the necessary probability model.

The class of output languages of deterministic tree-walking transducers is known to be equal to the class of yields of images of the regular tree languages under finite-copying top-down [r]

Abstract—Sticker systems and Watson-Crick automata are two modellings of DNA molecules in DNA computing. A sticker system is a computational model which is coded with single and double-stranded DNA molecules; while Watson-Crick automata is the automata counterpart of sticker system which represents the biological properties of DNA. Both of these models use the fea- ture of Watson-Crick complementarity in DNA computing. Previously, the **grammar** counterpart of the Watson-Crick automata have been introduced, known as Watson-Crick grammars which are classified into three classes: Wat- son-Crick regular grammars, Watson-Crick linear grammars and Watson-Crick **context**-**free** grammars. In this research, a new variant of Watson-Crick gram- mar called a static Watson-Crick **context**-**free** **grammar**, which is a **grammar** counterpart of sticker systems that generates the double-stranded strings and us- es rule as in **context**-**free** **grammar**, is introduced. The static Watson-Crick con- text-**free** **grammar** differs from a dynamic Watson-Crick **context**-**free** **grammar** in generating double-stranded strings, as well as for regular and linear gram- mars. The main result of the paper is to determine the generative powers of stat- ic Watson-Crick **context**-**free** grammars. Besides, the relationship of the fami- lies of languages generated by Chomsky grammars, sticker systems and Wat- son-Crick grammars are presented in terms of their hierarchy.

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1978b Evaluating English sentences in a logical model, presented to the 7th Inter- national Conference on Computation Linguistics, University of Bergen, Norway August 14-18.. Ann Arbor, [r]

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cally focus on the variable-**free** semantic represen- tations, as shown in Figure 1. On the target side, we convert these meaning representations to series of strings similar to NL. To do so, we simply take a preorder traversal of every functional form, and la- bel every function with the number of arguments it takes. Figure 1(b) shows an example of con- verted meaning representation, where each token is in the format of A@B where A is the symbol while B is either s indicating that the symbol is a string or a number indicating the symbol’s arity (constants, including strings, are treated as zero- argument functions).

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Next, consider the automata theoretic characterization of a regular language by means of a right-linear **grammar**. In process theory, a **grammar** is called a recursive specification: it is a set of recursive equations over a set of variables. A right-linear **grammar** then coincides with a recursive specification over a finite set of variables in the Minimal Algebra MA. (We use standard process algebra notation as propagated.)