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The equivalence problem of multitape finite automata

T. Harju, J. Karhumäki
1991 Theoretical Computer Science  
Intruductiou One of the oldest and most famous problems in automata theory is the equivalence problem for deterministic multitape finite automata.  ...  As a corollas we solve a long standing open problem in automata theow. namely, the equivalence problem for multitape deterministic finite automata.  ...  Acknowledgment The authors are grateful to G. Duchamp and J. Sakarovitch for their critical comments which improved the presentation of this paper.  ... 
doi:10.1016/0304-3975(91)90356-7 fatcat:7v6fmoygjvacph4nzxjcakfu4a

Page 2672 of Mathematical Reviews Vol. , Issue 82f [page]

1982 Mathematical Reviews  
Weak equivalence of finite automata is defined on the basis of it and a determination is made of the properties of weakly equivalent finite automata.  ...  The author observes that it is possible to find natural subclasses of finite multitape automata with solvable inclusion problem despite the fact that the general problem is unsolvable.  ... 

HOW TO SYNCHRONIZE THE HEADS OF A MULTITAPE AUTOMATON

OSCAR H. IBARRA, NICHOLAS Q. TRAN
2013 International Journal of Foundations of Computer Science  
In this paper, we exhibit various classes of multitape automata which can(not) be converted to equivalent synchronized multitape automata.  ...  In two recent papers, we looked at the problem of deciding, given an n-tape automaton of a given type, whether there exists an equivalent synchronized n-tape automaton of the same type.  ...  Introduction Motivated by reachability analyses of string programs using multitrack finitestate automata [9], we recently introduced and studied multitape finite automata whose heads are k-synchronized  ... 
doi:10.1142/s0129054113400194 fatcat:uqyyzwhjqvfcjnnhn3o4kqa42a

Revisiting the Equivalence Problem for Finite Multitape Automata [article]

James Worrell
2013 arXiv   pre-print
The decidability of determining equivalence of deterministic multitape automata (or transducers) was a longstanding open problem until it was resolved by Harju and Karhumäki in the early 1990s.  ...  From our proof we obtain a simple randomised algorithm for deciding language equivalence of deterministic multitape automata and, more generally, multiplicity equivalence of nondeterministic multitape  ...  Acknowledgments The author is grateful to Louis Rowen for helpful pointers in the proof of Proposition 2.  ... 
arXiv:1303.6704v2 fatcat:3gu3e5z2qrfl3hf3escsvpyziu

Revisiting the Equivalence Problem for Finite Multitape Automata [chapter]

James Worrell
2013 Lecture Notes in Computer Science  
The decidability of determining equivalence of deterministic multitape automata (or transducers) was a longstanding open problem until it was resolved by Harju and Karhumäki in the early 1990s.  ...  From our proof we obtain a simple randomised algorithm for deciding language equivalence of deterministic multitape automata and, more generally, multiplicity equivalence of nondeterministic multitape  ...  Acknowledgments The author is grateful to Louis Rowen for helpful pointers in the proof of Proposition 2.  ... 
doi:10.1007/978-3-642-39212-2_38 fatcat:7sahmfxpqngl5i3ry6amlaeumm

The equivalence problem of multidimensional multitape automata

Haik Grigorian, Samvel Shoukourian
2008 Journal of computer and system sciences (Print)  
It is shown that this problem can be reduced to the equivalence problem of ordinary multitape automata. Some applications of the result are adduced.  ...  This article considers the equivalence problem of multitape automata with multidimensional tapes, where the motion of the heads is monotone in all directions (no backward motion).  ...  Letichevsky, who outlined the general direction of investigations more than 30 years ago, Professor D.  ... 
doi:10.1016/j.jcss.2008.02.006 fatcat:xk7qjf5cxbc6phqaposl2hhqwm

Page 1016 of Mathematical Reviews Vol. 52, Issue 3 [page]

1976 Mathematical Reviews  
Clearly, the marker automata are equivalent to multi-head finite automata, where the same problems arise and have been studied.  ...  The authors study finite automata augmented with (a fixed number of) markers that the automata can move about on their input tapes.  ... 

MEASUREMENT OF DISTANCE BETWEEN REGULAR EVENTS FOR MULTITAPE AUTOMATA BASED ON A NEW CHARACTERIZATION OF EQUIVALENCE CLASSES

Tigran A. Grigoryan, Murad S. Hayrapetyan
2021 Proceedings of the YSU A: Physical and Mathematical Sciences  
In this paper several problems related to the implementation of the method for the approximate calculation of distance between regular events for multitape finite automata are considered and resolved.  ...  An algorithm of matching for the considered regular expressions is suggested and results of the algorithm application to some specific regular expressions are adduced.  ...  The problem of equivalence for multitape finite automata is generally not solvable [1] , hence the problem of whether d H (E 1 , E 2 ) = 0 is not solvable.  ... 
doi:10.46991/pysu:a/2021.55.1.072 fatcat:e3tehlj65rejviuigjasb6wupm

Page 1435 of Mathematical Reviews Vol. 39, Issue 6 [page]

1970 Mathematical Reviews  
One hierarchy is given in terms of three known types of nondeterministic multitape Turing machine : the general Turing machine, linear-bounded automaton and the two-way multitape finite automaton.  ...  From the author’s introduction: “The purpose of this paper is to prove the equivalence of two hierarchies of predicates.  ... 

An Approximate Method for Calculating the Distance Between Regular Languages for Multitape Finite Automata

Tigran Grigoryan
2020 Mathematical Problems of Computer Science  
Sets of word tuples, accepted by multitape finite automata and a metric space for languages accepted by these automata, are considered.  ...  An algorithm is proposed for calculating the introduced distance between regular languages accepted by multitape finite automata.  ...  Scott introduced deterministic multitape finite automata and the problem of equivalence for these automata [1] .  ... 
doi:10.51408/1963-0060 fatcat:uuejdkvt2bbejkidnucuzt6s5m

Introduction to the Theory of Computation

Michael Sipser
1996 ACM SIGACT News  
37 Formal definition of computation 40 Designing finite automata 41 The regular operations 44 1.2 Nondeterminism 47 Formal definition of a nondeterministic finite automaton . ... 53 Equivalence  ...  22 Exercises, Problems, and Solutions 25 Part One: Automata and Languages 29 1 Regular Languages 31 1.1 Finite Automata 31 Formal definition of a finite automaton 35 Examples of finite automata  ... 
doi:10.1145/230514.571645 fatcat:wkcpm5qh5vavlf23rkn5axvxxu

Rewrite Rule Grammars with Multitape Automata

Mans Hulden
2017 Journal of Language Modelling  
Keywords: grammar design, multitape automata, morphology, phonology, finite-state phonology The majority of computational implementations of phonological and morphophonological alternations rely on composing  ...  A model and a practical implementation of multitape automata is provided together with a multitape composition algorithm tailored to the representation used in this paper.  ...  Figure 4 illustrates different but equivalent outputs for the composition of two multitape automata.  ... 
doi:10.15398/jlm.v5i1.158 fatcat:eb5ncnuwsbaz7p2bjc7mxwkb24

Page 2438 of Mathematical Reviews Vol. 57, Issue 6 [page]

1979 Mathematical Reviews  
From the summary: “No solution has been given for the problem of deciding equivalence in general between deterministic push- down automata.  ...  From the summary: “In this paper we give a review of some of the recent results achieved when multitape automata are considered as accepting devices for languages.  ... 

Page 321 of Mathematical Reviews Vol. 43, Issue 1 [page]

1972 Mathematical Reviews  
) nondeterministic automata, as well as problems of stability.  ...  Topics covered include equivalence and | reduction, analysis and synthesis of finite automata (i.e., (le but étant l’application du langage dans les domaines de l'étude de la pédagogie des mathématiques  ... 

Page 951 of Mathematical Reviews Vol. 55, Issue 3 [page]

1978 Mathematical Reviews  
Author’s summary: “The equivalence problem for languages accepted by deterministic pushdown automata is shown to be decidable if and only if the strong equivalence problem for monadic recursion schemes  ...  In the condensed style of the author, the most important results on the difficulty in com- binatorial problems, finite numerical problems and non-finite numerical problems are summarised in three pages  ... 
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