Complexity of probabilistic versus deterministic automata

2005 ◽  
pp. 565-613 ◽  
Author(s):  
RūsiņŠ Freivalds
Keyword(s):  
Deterministic Automata

scholarly journals Coinductive Algorithms for Büchi Automata

2021 ◽  
Vol 180 (4) ◽  
pp. 351-373
Author(s):  
Denis Kuperberg ◽  
Laureline Pinault ◽  
Damien Pous
Keyword(s):  
State Space ◽  
State Of The Art ◽  
The State ◽  
Specific Structure ◽  
Büchi Automata ◽  
Deterministic Automata ◽  
Buchi Automata ◽  
Language Equivalence ◽  
Art Techniques

We propose a new algorithm for checking language equivalence of non-deterministic Büchi automata. We start from a construction proposed by Calbrix, Nivat and Podelski, which makes it possible to reduce the problem to that of checking equivalence of automata on finite words. Although this construction generates large and highly non-deterministic automata, we show how to exploit their specific structure and apply state-of-the art techniques based on coinduction to reduce the state-space that has to be explored. Doing so, we obtain algorithms which do not require full determinisation or complementation.

scholarly journals Copyful Streaming String Transducers

2021 ◽  
Vol 178 (1-2) ◽  
pp. 59-76
Author(s):  
Emmanuel Filiot ◽  
Pierre-Alain Reynier
Keyword(s):  
Polynomial Time ◽  
Equivalence Problem ◽  
Expressive Power ◽  
The Other ◽  
Finite State Automata ◽  
Finite State ◽  
Variable Content ◽  
Deterministic Automata ◽  
Intermediate Output ◽  
Linear Manner

Copyless streaming string transducers (copyless SST) have been introduced by R. Alur and P. Černý in 2010 as a one-way deterministic automata model to define transductions of finite strings. Copyless SST extend deterministic finite state automata with a set of variables in which to store intermediate output strings, and those variables can be combined and updated all along the run, in a linear manner, i.e., no variable content can be copied on transitions. It is known that copyless SST capture exactly the class of MSO-definable string-to-string transductions, and are as expressive as deterministic two-way transducers. They enjoy good algorithmic properties. Most notably, they have decidable equivalence problem (in PSpace). On the other hand, HDT0L systems have been introduced for a while, the most prominent result being the decidability of the equivalence problem. In this paper, we propose a semantics of HDT0L systems in terms of transductions, and use it to study the class of deterministic copyful SST. Our contributions are as follows: (i)HDT0L systems and total deterministic copyful SST have the same expressive power, (ii)the equivalence problem for deterministic copyful SST and the equivalence problem for HDT0L systems are inter-reducible, in quadratic time. As a consequence, equivalence of deterministic SST is decidable, (iii)the functionality of non-deterministic copyful SST is decidable, (iv)determining whether a non-deterministic copyful SST can be transformed into an equivalent non-deterministic copyless SST is decidable in polynomial time.

DETERMINISTIC AUTOMATA AND THE MONADIC THEORY OF ORDINALS < ω2

1983 ◽  
Vol 29 (5) ◽  
pp. 313-336 ◽  
Author(s):  
J. Richard Büchi ◽  
Charles Zaiontz
Keyword(s):  
Monadic Theory ◽  
Deterministic Automata

Descriptional Complexity of the Forever Operator

2019 ◽  
Vol 30 (01) ◽  
pp. 115-134 ◽  
Author(s):  
Michal Hospodár ◽  
Galina Jirásková ◽  
Peter Mlynárčik
Keyword(s):  
Regular Language ◽  
Finite Automata ◽  
Deterministic Finite Automata ◽  
State Complexity ◽  
Descriptional Complexity ◽  
Trade Offs ◽  
Number Formula ◽  
Deterministic Automata ◽  
Initial States ◽  
Nondeterministic State

We examine the descriptional complexity of the forever operator, which assigns the language [Formula: see text] to a regular language [Formula: see text], and we investigate the trade-offs between various models of finite automata. We consider complete and partial deterministic finite automata, nondeterministic finite automata with single or multiple initial states, alternating, and Boolean finite automata. We assume that the argument and the result of this operation are accepted by automata belonging to one of these six models. We investigate all possible trade-offs and provide a tight upper bound for 32 of 36 of them. The most interesting result is the trade-off from nondeterministic to deterministic automata given by the Dedekind number [Formula: see text]. We also prove that the nondeterministic state complexity of [Formula: see text] is [Formula: see text] which solves an open problem stated by Birget [The state complexity of [Formula: see text] and its connection with temporal logic, Inform. Process. Lett. 58 (1996) 185–188].

scholarly journals Processing XML streams with deterministic automata and stream indexes

2004 ◽  
Vol 29 (4) ◽  
pp. 752-788 ◽  
Author(s):  
Todd J. Green ◽  
Ashish Gupta ◽  
Gerome Miklau ◽  
Makoto Onizuka ◽  
Dan Suciu
Keyword(s):  
Deterministic Automata ◽  
Xml Streams

scholarly journals Deterministic automata for extended regular expressions

2017 ◽  
Vol 7 (1) ◽  
pp. 24-28
Author(s):  
Mirzakhmet Syzdykov
Keyword(s):  
Finite Automaton ◽  
Regular Languages ◽  
Regular Expressions ◽  
Deterministic Finite Automaton ◽  
Past Work ◽  
The Past ◽  
Deterministic Automata ◽  
Extended Regular Expressions

Abstract In this work we present the algorithms to produce deterministic finite automaton (DFA) for extended operators in regular expressions like intersection, subtraction and complement. The method like “overriding” of the source NFA(NFA not defined) with subset construction rules is used. The past work described only the algorithm for AND-operator (or intersection of regular languages); in this paper the construction for the MINUS-operator (and complement) is shown.

Two-way deterministic automata with two reversals are exponentially more succinct than with one reversal

2010 ◽  
Vol 110 (10) ◽  
pp. 396-398 ◽  
Author(s):  
Marcin Balcerzak ◽  
Damian Niwiński
Keyword(s):  
Deterministic Automata
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