581 research outputs found

    A Combinatorial Approach to Collapsing Words

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    Image reducing words and subgroups of free groups

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    AbstractA word w over a finite alphabet Σ is said to be n-collapsing if for an arbitrary finite automaton A=〈Q,Σ−·−〉, the inequality |Q·w|⩽|Q|−n holds provided that |Q·u|⩽|Q|−n for some word u (depending on A). We give an algorithm to test whether a word is 2-collapsing. To this aim we associate to every word w a finite family of finitely generated subgroups in finitely generated free groups and prove that the property of being 2-collapsing reflects in the property that each of these subgroups has index at most 2 in the corresponding free group. We also find a similar characterization for the closely related class of so-called 2-synchronizing words

    On the length of shortest 2-collapsing words

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    Automata, Logic and Semantic

    Pictorial Narratives and Temporal Refinement

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    Refinements are proposed to the default reading of two successive pictures p,p' as p and then p'. The refinements are based on the Aristotelian dictum, no time without change, and the principle of inertia, no change without force, guided by the adage, a picture's worth a thousand words. Words describing pictures are formalized as predicates, some stative and some non-stative (expressing forces), and interpreted (in either case) over strings qua models, subject to finite-state projections supporting variable granularity. A form of string iconicity is explored, with an eye to more transparent representations

    Solutions of Word Equations over Partially Commutative Structures

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    We give NSPACE(n log n) algorithms solving the following decision problems. Satisfiability: Is the given equation over a free partially commutative monoid with involution (resp. a free partially commutative group) solvable? Finiteness: Are there only finitely many solutions of such an equation? PSPACE algorithms with worse complexities for the first problem are known, but so far, a PSPACE algorithm for the second problem was out of reach. Our results are much stronger: Given such an equation, its solutions form an EDT0L language effectively representable in NSPACE(n log n). In particular, we give an effective description of the set of all solutions for equations with constraints in free partially commutative monoids and groups

    The design, implementation, and effectiveness of a Farsi word stemmer

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    A stemmer for the Farsi language has been designed, implemented, and evaluated. The stemmer uses Farsi morphology to remove affixes, producing effective stems. The implementation is written in C, using strings of unicode-encoded characters to represent Farsi words. It is meant to enhance the Farsi information retrieval system currently being developed at the Information Science Research Institute at the University of Nevada at Las Vegas. The effectiveness of the Farsi stemmer and stopword list on recall/precision was tested

    Synchronization of finite automata

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    A survey of the state-of-the-art of the theory of synchronizing automata is given in its part concerned with the case of complete deterministic automata. Algorithmic and complexity-theoretic aspects are considered, the existing results related to Černý’s conjecture and methods for their derivation are presented. Bibliography: 193 titles. © 2022 Russian Academy of Sciences, Steklov Mathematical Institute of RAS.Russian Foundation for Basic Research, РФФИ, (19-11-50120)Ministry of Education and Science of the Russian Federation, Minobrnauka, (FEUZ-2020-0016)This research was supported by the Russian Foundation for Basic Research under grant no. 19-11-50120 and by the Ministry of Science and Higher Education of the Russian Federation (project no. FEUZ-2020-0016)
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