Characterization of lattice-valued multiset finite automata

2021 ◽  
Author(s):  
M. K. Dubey ◽  
Anand P. Singh ◽  
Mallika Dhingra
Keyword(s):  
Finite Automata

A CHARACTERIZATION OF RECOGNIZABLE PICTURE LANGUAGES

1994 ◽  
Vol 08 (02) ◽  
pp. 501-508 ◽  
Author(s):  
KATSUSHI INOUE ◽  
ITSUO TAKANAMI
Keyword(s):  
Finite Automata ◽  
Two Dimensional ◽  
Open Problems ◽  
Nondeterministic Finite Automata ◽  
Letter Alphabet ◽  
The Family ◽  
On Line ◽  
Picture Languages

This paper first shows that REC, the family of recognizable picture languages in Giammarresi and Restivo,3 is equal to the family of picture languages accepted by two-dimensional on-line tessellation acceptors in Inoue and Nakamura.5 By using this result, we then solve open problems in Giammarresi and Restivo,3 and show that (i) REC is not closed under complementation, and (ii) REC properly contains the family of picture languages accepted by two-dimensional nondeterministic finite automata even over a one letter alphabet.

scholarly journals EFFICIENT DETERMINISTIC FINITE AUTOMATA SPLIT-MINIMIZATION DERIVED FROM BRZOZOWSKI'S ALGORITHM

2014 ◽  
Vol 25 (06) ◽  
pp. 679-696 ◽  
Author(s):  
PEDRO GARCÍA ◽  
DAMIÁN LÓPEZ ◽  
MANUEL VÁZQUEZ DE PARGA
Keyword(s):  
Computer Science ◽  
Finite Automata ◽  
Minimization Method ◽  
Deterministic Finite Automata ◽  
Classic Problem ◽  
Minimization Methods ◽  
Minimization Algorithms

Minimization of deterministic finite automata is a classic problem in Computer Science which is still studied nowadays. In this paper, we relate the different split-minimization methods proposed to date, or to be proposed, and the algorithm due to Brzozowski which has been usually set aside in any classification of DFA minimization algorithms. In our work, we first propose a polynomial minimization method derived from a paper by Champarnaud et al. We also show how the consideration of some efficiency improvements on this algorithm lead to obtain an algorithm similar to Hopcroft's classic algorithm. The results obtained lead us to propose a characterization of the set of possible splitters.

scholarly journals Languages recognized by nondeterministic quantum finite automata

2010 ◽  
Vol 10 (9&10) ◽  
pp. 747-770
Author(s):  
Abuzer Yakaryilmaz ◽  
A.C. Cem Say
Keyword(s):  
Finite Automaton ◽  
Finite Automata ◽  
Space Complexity ◽  
Complexity Classes ◽  
Language Recognition ◽  
Closure Properties ◽  
Quantum Finite Automata ◽  
Sublogarithmic Space

The nondeterministic quantum finite automaton (NQFA) is the only known case where a one-way quantum finite automaton (QFA) model has been shown to be strictly superior in terms of language recognition power to its probabilistic counterpart. We give a characterization of the class of languages recognized by NQFAs, demonstrating that it is equal to the class of exclusive stochastic languages. We also characterize the class of languages that are recognized necessarily by two-sided error by QFAs. It is shown that these classes remain the same when the QFAs used in their definitions are replaced by several different model variants that have appeared in the literature. We prove several closure properties of the related classes. The ramifications of these results about classical and quantum sublogarithmic space complexity classes are examined.

GENERAL ALGORITHMS FOR TESTING THE AMBIGUITY OF FINITE AUTOMATA AND THE DOUBLE-TAPE AMBIGUITY OF FINITE-STATE TRANSDUCERS

2011 ◽  
Vol 22 (04) ◽  
pp. 883-904 ◽  
Author(s):  
CYRIL ALLAUZEN ◽  
MEHRYAR MOHRI ◽  
ASHISH RASTOGI
Keyword(s):  
General Problem ◽  
Finite Automata ◽  
General Algorithm ◽  
Approximate Computation ◽  
Probabilistic Automaton ◽  
Bounded Delay ◽  
Finite State Transducers ◽  
Specific Analysis ◽  
Finite State

We present efficient algorithms for testing the finite, polynomial, and exponential ambiguity of finite automata with ε-transitions. We give an algorithm for testing the exponential ambiguity of an automaton A in time [Formula: see text], and finite or polynomial ambiguity in time [Formula: see text], where |A|E denotes the number of transitions of A. These complexities significantly improve over the previous best complexities given for the same problem. Furthermore, the algorithms presented are simple and based on a general algorithm for the composition or intersection of automata. Additionally, we give an algorithm to determine in time [Formula: see text] the degree of polynomial ambiguity of a polynomially ambiguous automaton A and present an application of our algorithms to an approximate computation of the entropy of a probabilistic automaton. We also study the double-tape ambiguity of finite-state transducers. We show that the general problem is undecidable and that it is NP-hard for acyclic transducers. We present a specific analysis of the double-tape ambiguity of transducers with bounded delay. In particular, we give a characterization of double-tape ambiguity for synchronized transducers with zero delay that can be tested in quadratic time and give an algorithm for testing the double-tape ambiguity of transducers with bounded delay.

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

2021 ◽  
Vol 55 (1 (254)) ◽  
pp. 72-80
Author(s):  
Tigran A. Grigoryan ◽  
Murad S. Hayrapetyan
Keyword(s):  
Approximate Calculation ◽  
Finite Automata ◽  
Equivalence Classes ◽  
Regular Expressions

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 proposed method can be used not only for the mentioned implementation, but also separately.

Minimal Reversible Deterministic Finite Automata

2018 ◽  
Vol 29 (02) ◽  
pp. 251-270 ◽  
Author(s):  
Markus Holzer ◽  
Sebastian Jakobi ◽  
Martin Kutrib
Keyword(s):  
Lower Bounds ◽  
Finite Automata ◽  
Transition Function ◽  
Upper And Lower Bounds ◽  
State Graph ◽  
Deterministic Finite Automata ◽  
Injective Mapping ◽  
Pattern Approach ◽  
Almost All

We study reversible deterministic finite automata (REV-DFAs), that are partial deterministic finite automata whose transition function induces an injective mapping on the state set for every letter of the input alphabet. We give a structural characterization of regular languages that can be accepted by REV-DFAs. This characterization is based on the absence of a forbidden pattern in the (minimal) deterministic state graph. Again with a forbidden pattern approach, we also show that the minimality of REV-DFAs among all equivalent REV-DFAs can be decided. Both forbidden pattern characterizations give rise to [Formula: see text]-complete decision algorithms. In fact, our techniques allow us to construct the minimal REV-DFA for a given minimal DFA. These considerations lead to asymptotic upper and lower bounds on the conversion from DFAs to REV-DFAs. Thus, almost all problems that concern uniqueness and the size of minimal REV-DFAs are solved.

A Logical Characterization of Small 2NFAs

2017 ◽  
Vol 28 (05) ◽  
pp. 445-464
Author(s):  
Christos A. Kapoutsis ◽  
Lamana Mulaffer
Keyword(s):  
Transitive Closure ◽  
Closure Operator ◽  
Finite Automata ◽  
Disjunctive Normal Form ◽  
Order Logic ◽  
First Order Logic ◽  
First Order ◽  
Polynomial Size ◽  
Fixed Input

Let 2N be the class of families of problems solvable by families of two-way nondeterministic finite automata of polynomial size. We characterize 2N in terms of families of formulas of transitive-closure logic. These formulas apply the transitive-closure operator on a quantifier-free disjunctive normal form of first-order logic with successor and constants, where (i) apart from two special variables, all others are equated to constants in every clause, and (ii) no clause simultaneously relates these two special variables and refers to fixed input cells. We prove that automata with polynomially many states are as powerful as formulas with polynomially many clauses and polynomially large constants. This can be seen as a refinement of Immerman’s theorem that nondeterministic logarithmic space matches positive transitive-closure logic ([Formula: see text]).

FINITE AUTOMATA OVER FREE GROUPS

2000 ◽  
Vol 10 (06) ◽  
pp. 725-737 ◽  
Author(s):  
JÜRGEN DASSOW ◽  
VICTOR MITRANA
Keyword(s):  
Free Group ◽  
Finite Automata ◽  
Free Groups ◽  
Input String ◽  
Neutral Element ◽  
Deterministic Case ◽  
Final Configuration ◽  
Context Free

Finite automata are extended by adding an element of a given group to each of their configurations. An input string is accepted if and only if the neutral element of the group is associated to a final configuration reached by the automaton. We get a new characterization of the context-free languages as soon as the considered group is the binary free group. The result cannot be carried out in the deterministic case. Some remarks about finite automata over other groups are also presented.

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