Image reducing words and subgroups of free groups

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

Automata, Logic and Semantic

Pictorial Narratives and Temporal Refinement

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

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

Abbreviated text input using language modeling.

We address the problem of improving the efficiency of natural language text input under degraded conditions (for instance, on mobile computing devices or by disabled users), by taking advantage of the informational redundancy in natural language. Previous approaches to this problem have been based on the idea of prediction of the text, but these require the user to take overt action to verify or select the system’s predictions. We propose taking advantage of the duality between prediction and compression. We allow the user to enter text in compressed form, in particular, using a simple stipulated abbreviation method that reduces characters by 26.4%, yet is simple enough that it can be learned easily and generated relatively fluently. We decode the abbreviated text using a statistical generative model of abbreviation, with a residual word error rate of 3.3%. The chief component of this model is an n-gram language model. Because the system’s operation is completely independent from the user’s, the overhead from cognitive task switching and attending to the system’s actions online is eliminated, opening up the possibility that the compression-based method can achieve text input efficiency improvements where the prediction-based methods have not. We report the results of a user study evaluating this method.Engineering and Applied Science

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

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

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)