Модели вычислений с однозначным покрытием

Рассматриваются модели вычислений: конечные детерминированные и многоленточные автоматы. Описывается процедура построения по любому автомату модели ему эквивалентного с однозначным покрытиемyesБелГ

Модели вычислений с однозначным покрытием

Рассматриваются модели вычислений: конечные детерминированные и многоленточные автоматы. Описывается процедура построения по любому автомату модели ему эквивалентного с однозначным покрытие

The inclusion problem for simple languages

AbstractA deterministic pushdown acceptor is called a simple machine when it is restricted to have only one state, operate in real-time, and accept by empty store. While the existence of an effective procedure for deciding equivalence of languages accepted by these simple machines is well-known, it is shown that this family is powerful enough to have an undecidable inclusion problem. It follows that the inclusion problems for the LL(k) languages and the free monadic recursion schemes that do not use an identity function are also undecidable

Минимизация информационных структур с почти коммутативными свойствами

Решение фундаментальных проблем информационных структур с почти коммутативными свойствами, минимизации эквивалентных преобразований и эквивалентности для подклассов информационных структу

On Equivalence and Uniformisation Problems for Finite Transducers

Transductions are binary relations of finite words. For rational transductions, i.e., transductions defined by finite transducers, the inclusion, equivalence and sequential uniformisation problems are known to be undecidable. In this paper, we investigate stronger variants of inclusion, equivalence and sequential uniformisation, based on a general notion of transducer resynchronisation, and show their decidability. We also investigate the classes of finite-valued rational transductions and deterministic rational transductions, which are known to have a decidable equivalence problem. We show that sequential uniformisation is also decidable for them

Equivalence Testing of Weighted Automata over Partially Commutative Monoids

Motivated by equivalence testing of k-tape automata, we study the equivalence testing of weighted automata in the more general setting, over partially commutative monoids (in short, pc monoids), and show efficient algorithms in some special cases, exploiting the structure of the underlying non-commutation graph of the monoid. Specifically, if the edge clique cover number of the non-commutation graph of the pc monoid is a constant, we obtain a deterministic quasi-polynomial time algorithm for equivalence testing. As a corollary, we obtain the first deterministic quasi-polynomial time algorithms for equivalence testing of k-tape weighted automata and for equivalence testing of deterministic k-tape automata for constant k. Prior to this, the best complexity upper bound for these k-tape automata problems were randomized polynomial-time, shown by Worrell [James Worrell, 2013]. Finding a polynomial-time deterministic algorithm for equivalence testing of deterministic k-tape automata for constant k has been open for several years [Emily P. Friedman and Sheila A. Greibach, 1982] and our results make progress. We also consider pc monoids for which the non-commutation graphs have an edge cover consisting of at most k cliques and star graphs for any constant k. We obtain a randomized polynomial-time algorithm for equivalence testing of weighted automata over such monoids. Our results are obtained by designing efficient zero-testing algorithms for weighted automata over such pc monoids

Revisiting the Equivalence Problem for Finite Multitape Automata

Abstract. The decidability of determining equivalence of deterministic multitape automata was a longstanding open problem until it was resolved by Harju and Karhumäki in the early 1990s. Their proof of decidability yields a co-NP upper bound, but apparently not much more is known about the complexity of the problem. In this paper we give an alternative proof of decidability which follows the basic strategy of Harju and Karhumäki, but replaces their use of group theory with results on matrix algebras. From our proof we obtain a simple randomised algorithm for deciding equivalence of deterministic multitape automata, as well as automata with transition weights in the field of rational numbers. The algorithm involves only matrix exponentiation and runs in polynomial time for each fixed number of tapes. If the two input automata are inequivalent then the algorithm outputs a word on which they differ

Decision Problems for Subclasses of Rational Relations over Finite and Infinite Words

We consider decision problems for relations over finite and infinite words defined by finite automata. We prove that the equivalence problem for binary deterministic rational relations over infinite words is undecidable in contrast to the case of finite words, where the problem is decidable. Furthermore, we show that it is decidable in doubly exponential time for an automatic relation over infinite words whether it is a recognizable relation. We also revisit this problem in the context of finite words and improve the complexity of the decision procedure to single exponential time. The procedure is based on a polynomial time regularity test for deterministic visibly pushdown automata, which is a result of independent interest.Comment: v1: 31 pages, submitted to DMTCS, extended version of the paper with the same title published in the conference proceedings of FCT 2017; v2: 32 pages, minor revision of v1 (DMTCS review process), results unchanged; v3: 32 pages, enabled hyperref for Figure 1; v4: 32 pages, add reference for known complexity results for the slenderness problem; v5: 32 pages, added DMTCS metadat