scholarly journals One-way Resynchronizability of Word Transducers

2021 ◽  
pp. 124-143
Author(s):  
Sougata Bose ◽  
S. N. Krishna ◽  
Anca Muscholl ◽  
Gabriele Puppis
Keyword(s):  
Decidability Result

AbstractThe origin semantics for transducers was proposed in 2014, and it led to various characterizations and decidability results that are in contrast with the classical semantics. In this paper we add a further decidability result for characterizing transducers that are close to one-way transducers in the origin semantics. We show that it is decidable whether a non-deterministic two-way word transducer can be resynchronized by a bounded, regular resynchronizer into an origin-equivalent one-way transducer. The result is in contrast with the usual semantics, where it is undecidable to know if a non-deterministic two-way transducer is equivalent to some one-way transducer.

A decidability result in algebraic language theory

1974 ◽  
Vol 8 (3) ◽  
pp. 225-227
Author(s):  
Robert Townsend
Keyword(s):  
Language Theory ◽  
Decidability Result ◽  
Algebraic Language

scholarly journals A decidability result for the dominating set problem

2010 ◽  
Vol 411 (44-46) ◽  
pp. 4023-4027 ◽  
Author(s):  
Vadim V. Lozin
Keyword(s):  
Dominating Set ◽  
Decidability Result ◽  
Dominating Set Problem

A decidability result for homomorphic representation of automata by 205-1205-1205-1

1989 ◽  
Vol 53 (1-2) ◽  
pp. 205-212
Author(s):  
Z. Ésik ◽  
F. Gécseg
Keyword(s):  
Decidability Result

scholarly journals Reasoning with Forest Logic Programs and f-hybrid knowledge bases

2011 ◽  
Vol 13 (3) ◽  
pp. 395-463
Author(s):  
CRISTINA FEIER ◽  
STIJN HEYMANS
Keyword(s):  
Answer Set Programming ◽  
Knowledge Bases ◽  
Logic Programs ◽  
Decidability Result ◽  
Tree Shape ◽  
Alternative Approach ◽  
Hybrid Framework ◽  
Hybrid Knowledge ◽  
Satisfiability Checking ◽  
Answer Set

AbstractOpen Answer Set Programming (OASP) is an undecidable framework for integrating ontologies and rules. Although several decidable fragments of OASP have been identified, few reasoning procedures exist. In this paper, we provide a sound, complete, and terminating algorithm for satisfiability checking w.r.t. Forest Logic Programs (FoLPs), a fragment of OASP where rules have a tree shape and allow for inequality atoms and constants. The algorithm establishes a decidability result for FoLPs. Although believed to be decidable, so far only the decidability for two small subsets of FoLPs, local FoLPs and acyclic FoLPs, has been shown. We further introduce f-hybrid knowledge bases, a hybrid framework where knowledge bases and FoLPs coexist, and we show that reasoning with such knowledge bases can be reduced to reasoning with FoLPs only. We note that f-hybrid knowledge bases do not require the usual (weakly) DL-safety of the rule component, thus providing a genuine alternative approach to current integration approaches of ontologies and rules.

scholarly journals Optimal Strategies in Priced Timed Game Automata

2004 ◽  
Vol 11 (4) ◽  
Author(s):  
Patricia Bouyer ◽  
Franck Cassez ◽  
Emmanuel Fleury ◽  
Kim G. Larsen
Keyword(s):  
Optimal Strategy ◽  
Optimal Strategies ◽  
Decidability Result ◽  
Optimal Cost

Priced timed (game) automata extends timed (game) automata with costs on both locations and transitions. In this paper we focus on reachability games for priced timed game automata and prove that the optimal cost for winning such a game is computable under conditions concerning the non-zenoness of cost. Under stronger conditions (strictness of constraints) we prove in addition that it is decidable whether there is an optimal strategy in which case an optimal strategy can be computed. Our results extend previous decidability result which requires the underlying game automata to be acyclic. Finally, our results are encoded in a first prototype in HyTech which is applied on a small case-study.

scholarly journals Quadratic Word Equations with Length Constraints, Counter Systems, and Presburger Arithmetic with Divisibility

2021 ◽  
Vol Volume 17, Issue 4 ◽  
Author(s):  
Anthony W. Lin ◽  
Rupak Majumdar
Keyword(s):  
Theoretical Foundation ◽  
Constraint Solving ◽  
Simple Loop ◽  
Decidability Result ◽  
Presburger Arithmetic ◽  
Existential Theory ◽  
Word Equation ◽  
Word Equations ◽  
Left And Right ◽  
Np Complete

Word equations are a crucial element in the theoretical foundation of constraint solving over strings. A word equation relates two words over string variables and constants. Its solution amounts to a function mapping variables to constant strings that equate the left and right hand sides of the equation. While the problem of solving word equations is decidable, the decidability of the problem of solving a word equation with a length constraint (i.e., a constraint relating the lengths of words in the word equation) has remained a long-standing open problem. We focus on the subclass of quadratic word equations, i.e., in which each variable occurs at most twice. We first show that the length abstractions of solutions to quadratic word equations are in general not Presburger-definable. We then describe a class of counter systems with Presburger transition relations which capture the length abstraction of a quadratic word equation with regular constraints. We provide an encoding of the effect of a simple loop of the counter systems in the existential theory of Presburger Arithmetic with divisibility (PAD). Since PAD is decidable (NP-hard and is in NEXP), we obtain a decision procedure for quadratic words equations with length constraints for which the associated counter system is flat (i.e., all nodes belong to at most one cycle). In particular, we show a decidability result (in fact, also an NP algorithm with a PAD oracle) for a recently proposed NP-complete fragment of word equations called regular-oriented word equations, when augmented with length constraints. We extend this decidability result (in fact, with a complexity upper bound of PSPACE with a PAD oracle) in the presence of regular constraints.

A BOUND ON THE NUMBER OF UNARY POLYNOMIAL FUNCTIONS AND A DECIDABILITY RESULT FOR NEAR-RINGS

2005 ◽  
Vol 15 (02) ◽  
pp. 279-289 ◽  
Author(s):  
ERHARD AICHINGER
Keyword(s):  
Polynomial Functions ◽  
Subdirectly Irreducible ◽  
Decidability Result ◽  
Expanded Group ◽  
Inner Automorphism

Given a finite zero-symmetric near-ring with identity N, we ask whether there is a group G such that N is isomorphic to the inner automorphism near-ring <I(G);+,◦>, or whether N is a compatible near-ring. We will show that there are algorithms that decide these questions. To this end, we study polynomial functions on subdirectly irreducible expanded groups. We prove that the size of a finite subdirectly irreducible expanded group is bounded from above by a function of the number of its zero-preserving unary polynomial functions.

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