STRICT LOCAL TESTABILITY OF THE FINITE CONTROL OF TWO-WAY AUTOMATA AND OF REGULAR PICTURE DESCRIPTION LANGUAGES

We prove that every regular language is recognized by a deterministic two-way finite automaton whose control unit is strictly locally testing. Similarly, every picture language which can be described by a regular language can actually be described by a strictly locally testable language; this strengthens a result of Friedhelra Hinz.

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STATE COMPLEXITY OF ADDITIVE WEIGHTED FINITE AUTOMATA

International Journal of Foundations of Computer Science ◽

10.1142/s0129054107005443 ◽

2007 ◽

Vol 18 (06) ◽

pp. 1407-1416 ◽

Cited By ~ 10

Author(s):

KAI SALOMAA ◽

PAUL SCHOFIELD

Keyword(s):

Upper Bound ◽

Finite Automaton ◽

Regular Language ◽

Finite Automata ◽

The State ◽

Deterministic Finite Automata ◽

State Complexity ◽

Weighted Finite Automata

It is known that the neighborhood of a regular language with respect to an additive distance is regular. We introduce an additive weighted finite automaton model that provides a conceptually simple way to reprove this result. We consider the state complexity of converting additive weighted finite automata to deterministic finite automata. As our main result we establish a tight upper bound for the state complexity of the conversion.

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State Complexity of Suffix Distance

International Journal of Foundations of Computer Science ◽

10.1142/s0129054119400355 ◽

2019 ◽

Vol 30 (06n07) ◽

pp. 1197-1216

Author(s):

Timothy Ng ◽

David Rappaport ◽

Kai Salomaa

Keyword(s):

Lower Bound ◽

Finite Automaton ◽

Regular Language ◽

Upper Bounds ◽

The State ◽

Deterministic Finite Automaton ◽

Tight Bound ◽

State Complexity

The neighbourhood of a regular language with respect to the prefix, suffix and subword distance is always regular and a tight bound for the state complexity of prefix distance neighbourhoods is known. We give upper bounds for the state complexity of the neighbourhood of radius [Formula: see text] of an [Formula: see text]-state deterministic finite automaton language with respect to the suffix distance and the subword distance, respectively. For restricted values of [Formula: see text] and [Formula: see text] we give a matching lower bound for the state complexity of suffix distance neighbourhoods.

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Seeing Is Slicing: Observation Based Slicing of Picture Description Languages

2014 IEEE 14th International Working Conference on Source Code Analysis and Manipulation ◽

10.1109/scam.2014.26 ◽

2014 ◽

Cited By ~ 5

Author(s):

Shin Yoo ◽

David Binkley ◽

Roger Eastman

Keyword(s):

Picture Description ◽

Description Languages

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Exponential diophantine equations in rings of positive characteristic

Journal of Knot Theory and Its Ramifications ◽

10.1142/s0218216520400027 ◽

2020 ◽

Vol 29 (02) ◽

pp. 2040002

Author(s):

A. A. Chilikov ◽

Alexey Belov-Kanel

Keyword(s):

Finite Automaton ◽

Regular Language ◽

Diophantine Equations ◽

Positive Characteristic ◽

Matrix Ring ◽

Exponential Diophantine Equations

In this paper, we prove an algorithmical solvability of exponential-Diophantine equations in rings represented by matrices over fields of positive characteristic. Consider the system of exponential-Diophantine equations [Formula: see text] where [Formula: see text] are constants from matrix ring of characteristic [Formula: see text], [Formula: see text] are indeterminates. For any solution [Formula: see text] of the system we construct a word (over an alphabet containing [Formula: see text] symbols) [Formula: see text] where [Formula: see text] is a [Formula: see text]-tuple [Formula: see text], [Formula: see text] is the [Formula: see text]th digit in the [Formula: see text]-adic representation of [Formula: see text]. The main result of this paper is following: the set of words corresponding in this sense to solutions of a system of exponential-Diophantine equations is a regular language (i.e., recognizable by a finite automaton). There exists an algorithm which calculates this language. This algorithm is constructed in the paper.

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A DECISION PROBLEM FOR ULTIMATELY PERIODIC SETS IN NONSTANDARD NUMERATION SYSTEMS

International Journal of Algebra and Computation ◽

10.1142/s0218196709005330 ◽

2009 ◽

Vol 19 (06) ◽

pp. 809-839 ◽

Cited By ~ 7

Author(s):

JASON BELL ◽

EMILIE CHARLIER ◽

AVIEZRI S. FRAENKEL ◽

MICHEL RIGO

Keyword(s):

Finite Automaton ◽

Regular Language ◽

Decision Problem ◽

Decision Procedure ◽

Fibonacci Sequence ◽

Finite Union ◽

Numeration System ◽

Periodic Sets ◽

Numeration Systems ◽

The One

Consider a nonstandard numeration system like the one built over the Fibonacci sequence where nonnegative integers are represented by words over {0,1} without two consecutive 1. Given a set X of integers such that the language of their greedy representations in this system is accepted by a finite automaton, we consider the problem of deciding whether or not X is a finite union of arithmetic progressions. We obtain a decision procedure for this problem, under some hypothesis about the considered numeration system. In a second part, we obtain an analogous decision result for a particular class of abstract numeration systems built on an infinite regular language.

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The Degree of Irreversibility in Deterministic Finite Automata

International Journal of Foundations of Computer Science ◽

10.1142/s0129054117400044 ◽

2017 ◽

Vol 28 (05) ◽

pp. 503-522

Author(s):

Holger Bock Axelsen ◽

Markus Holzer ◽

Martin Kutrib

Keyword(s):

Finite Automaton ◽

Regular Language ◽

Finite Automata ◽

Deterministic Finite Automaton ◽

Deterministic Finite Automata ◽

Infinite Hierarchy ◽

Complete Problem ◽

Nondeterministic Finite Automata ◽

Forbidden Patterns

Recently, a method to decide the NL-complete problem of whether the language accepted by a given deterministic finite automaton (DFA) can also be accepted by some reversible deterministic finite automaton (REV-DFA) has been derived. Here, we show that the corresponding problem for nondeterministic finite automata (NFA) is PSPACE-complete. The recent DFA method essentially works by minimizing the DFA and inspecting it for a forbidden pattern. We here study the degree of irreversibility for a regular language, the minimal number of such forbidden patterns necessary in any DFA accepting the language, and show that the degree induces a strict infinite hierarchy of language families. We examine how the degree of irreversibility behaves under the usual language operations union, intersection, complement, concatenation, and Kleene star, showing tight bounds (some asymptotically) on the degree.

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Parallel Algorithms for Minimal Nondeterministic Finite Automata Inference

Fundamenta Informaticae ◽

10.3233/fi-2021-2004 ◽

2021 ◽

Vol 178 (3) ◽

pp. 203-227

Author(s):

Tomasz Jastrzab ◽

Zbigniew J. Czech ◽

Wojciech Wieczorek

Keyword(s):

Parallel Algorithms ◽

Constraint Satisfaction ◽

Finite Automaton ◽

Regular Language ◽

Finite Automata ◽

Constraint Satisfaction Problem ◽

Computational Experiments ◽

Learning Sample ◽

Automata Inference ◽

Nondeterministic Finite Automaton

The goal of this paper is to develop the parallel algorithms that, on input of a learning sample, identify a regular language by means of a nondeterministic finite automaton (NFA). A sample is a pair of finite sets containing positive and negative examples. Given a sample, a minimal NFA that represents the target regular language is sought. We define the task of finding an NFA, which accepts all positive examples and rejects all negative ones, as a constraint satisfaction problem, and then propose the parallel algorithms to solve the problem. The results of comprehensive computational experiments on the variety of inference tasks are reported. The question of minimizing an NFA consistent with a learning sample is computationally hard.

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Finitely generated subgroups of free groups as formal languages and their cogrowth

10.46298/jgcc.2021.13.2.7617 ◽

2021 ◽

Vol volume 13, issue 2 ◽

Author(s):

Arman Darbinyan ◽

Rostislav Grigorchuk ◽

Asif Shaikh

Keyword(s):

Free Group ◽

Finite Automaton ◽

Finite Rank ◽

Regular Language ◽

Free Groups ◽

Formal Languages ◽

Finitely Generated ◽

Deterministic Finite Automaton ◽

Method Of Calculation ◽

Reduced Words

For finitely generated subgroups $H$ of a free group $F_m$ of finite rank $m$, we study the language $L_H$ of reduced words that represent $H$ which is a regular language. Using the (extended) core of Schreier graph of $H$, we construct the minimal deterministic finite automaton that recognizes $L_H$. Then we characterize the f.g. subgroups $H$ for which $L_H$ is irreducible and for such groups explicitly construct ergodic automaton that recognizes $L_H$. This construction gives us an efficient way to compute the cogrowth series $L_H(z)$ of $H$ and entropy of $L_H$. Several examples illustrate the method and a comparison is made with the method of calculation of $L_H(z)$ based on the use of Nielsen system of generators of $H$.

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