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The equivalence problem of multitape finite automata

1991
*
Theoretical Computer Science
*

Intruductiou One

doi:10.1016/0304-3975(91)90356-7
fatcat:7v6fmoygjvacph4nzxjcakfu4a
*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. ...##
###
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

2013
*
International Journal of Foundations of Computer Science
*

In this paper, we exhibit various classes

doi:10.1142/s0129054113400194
fatcat:uqyyzwhjqvfcjnnhn3o4kqa42a
*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 ...##
###
Revisiting the Equivalence Problem for Finite Multitape Automata
[article]

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. ...

##
###
Revisiting the Equivalence Problem for Finite Multitape Automata
[chapter]

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. ...

##
###
The equivalence problem of multidimensional multitape automata

2008
*
Journal of computer and system sciences (Print)
*

It is shown that this

doi:10.1016/j.jcss.2008.02.006
fatcat:xk7qjf5cxbc6phqaposl2hhqwm
*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. ...##
###
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

2021
*
Proceedings of the YSU A: Physical and Mathematical Sciences
*

In this paper several

doi:10.46991/pysu:a/2021.55.1.072
fatcat:e3tehlj65rejviuigjasb6wupm
*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. ...##
###
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

2020
*
Mathematical Problems of Computer Science
*

Sets

doi:10.51408/1963-0060
fatcat:uuejdkvt2bbejkidnucuzt6s5m
*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] . ...##
###
Introduction to the Theory of Computation

1996
*
ACM SIGACT News
*

37
Formal definition

doi:10.1145/230514.571645
fatcat:wkcpm5qh5vavlf23rkn5axvxxu
*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*...##
###
Rewrite Rule Grammars with Multitape Automata

2017
*
Journal of Language Modelling
*

Keywords: grammar design,

doi:10.15398/jlm.v5i1.158
fatcat:eb5ncnuwsbaz7p2bjc7mxwkb24
*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*. ...##
###
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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