The accepting power of finite automata over groups

Mitrana, Víctor; Stiebe, Ralf

doi:10.1007/3-540-62844-4_4

Cited by 18 publications

(24 citation statements)

References 4 publications

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“…There are many variants of counter automata and languages in the literature, see for example [2,8,9,11,15,17,18,22,36]. In this article we define a counter automaton as follows.…”

Section: Counter Automatamentioning

confidence: 99%

C-graph automatic groups

Elder

Taback

2014

Journal of Algebra

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Abstract. We generalize the notion of a graph automatic group introduced by Kharlampovich, Khoussainov and Miasnikov by replacing the regular languages in their definition with more powerful language classes. For a fixed language class C, we call the resulting groups C-graph automatic. We prove that the class of C-graph automatic groups is closed under change of generating set, direct and free product for certain classes C. We show that for quasirealtime counter-graph automatic groups where normal forms have length that is linear in the geodesic length, there is an algorithm to compute normal forms (and therefore solve the word problem) in polynomial time. The class of quasirealtime counter-graph automatic groups includes all Baumslag-Solitar groups, and the free group of countably infinite rank. Context-sensitive-graph automatic groups are shown to be a very large class, which encompasses, for example, groups with unsolvable conjugacy problem, the Grigorchuk group, and Thompson's groups F, T and V .

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“…There are many variants of counter automata and languages in the literature, see for example [2,8,9,11,15,17,18,22,36]. In this article we define a counter automaton as follows.…”

Section: Counter Automatamentioning

confidence: 99%

C-graph automatic groups

Elder

Taback

2014

Journal of Algebra

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“…We examine these machines under several different regimes, enabling us to determine the effect of definitional parameters such as whether the input is scanned in "real time" or pausing the head on an input symbol for several steps is allowed, whether the machine can read its register during computation or is "blind", with acceptance possible only if the register has returned to its initial value at the end, and whether nondeterminism confers any additional recognition power over deterministic programs. We demonstrate a close relationship between the nondeterministic one-way blind variant of the HVA model and the EFA's of [15], which we believe to be important for the following reasons.…”

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confidence: 64%

“…In this section, we will exploit a relationship between 1NBHVA(k)'s and the extended finite automata of [15] over free groups to demonstrate the power of homing vector automata.…”

Section: Relationship With Extended Finite Automatamentioning

confidence: 99%

Homing vector automata

Salehi

Say

D'Alessandro

2016

RAIRO-Theor. Inf. Appl.

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We introduce homing vector automata, which are finite automata augmented by a vector that is multiplied at each step by a matrix determined by the current transition, and have to return the vector to its original setting in order to accept the input. The computational power and properties of deterministic, nondeterministic, blind, non-blind, real-time and one-way versions of these machines are examined and compared to various related types of automata. A generalized version of the Stern-Brocot encoding method, suitable for representing strings on arbitrary alphabets, is also developed.

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“…These definitions are due to Mitrana and Striebe [9]. Note that in these counter automata, the values of the counters is not accessible until the final accept/fail state.…”

Section: Definitionsmentioning

confidence: 99%

G-automata, counter languages and the Chomsky hierarchy

Elder¹

2007

Groups St Andrews 2005

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We consider how the languages of G-automata compare with other formal language classes. We prove that if the word problem of G is accepted by a machine in the class M then the language of any G-automaton is in the class M. It follows that the so called counter languages (languages of Z n -automata) are context-sensitive, and further that counter languages are indexed if and only if the word problem for Z n is indexed.

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The accepting power of finite automata over groups

Cited by 18 publications

References 4 publications

C-graph automatic groups

C-graph automatic groups

Homing vector automata

G-automata, counter languages and the Chomsky hierarchy

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