In this paper we work over linearly ordered data domains equipped with finitely many unary predicates and constants. We consider nondeterministic automata processing words and storing finitely many variables ranging over the domain. During a transition, these automata can compare the data values of the current configuration with those of the previous configuration using the linear order, the un...

For each regular language L we describe a family of canonical nondeterministic acceptors (nfas). Their construction follows a uniform recipe: build the minimal dfa for L in a locally finite variety V , and apply an equivalence between the finite V-algebras and a category of finite structured sets and relations. By instantiating this to different varieties we recover three well-studied canonical...

It is shown that if a 2-way probabilistic nite state automaton (2pfa) M recognizes a nonregular language L with error probability bounded below 1/2, then there is a positive constant b (depending on M) such that, for innnitely many inputs x, the expected running time of M on input x must exceed 2 n b where n is the length of x. This complements a result of Freivalds showing that 2pfa's can reco...

We study the relationship between the sizes of two-way finite automata accepting a language and its complement. In the deterministic case, for a given automaton (2dfa) with n states, we build an automaton accepting the complement with at most 4n states, independently of the size of the input alphabet. Actually, we show a stronger result, by presenting an equivalent 4n-state 2dfa that always hal...

In this paperwe adapt thewell-knownBrzozowskideterminizationmethod to fuzzy automata. Thismethod gives better results than all previously knownmethods for determinization of fuzzy automata developed by Bělohlávek [InformSciences 143 (2002)205–209],Li andPedrycz [FuzzySet Syst 156 (2005)68–92], Ignjatović et al. [Inform Sciences 178 (2008) 164–180], and Jančić et al. [Inform Sciences 181 (2011) ...

GP (for Graph Programs) is a rule-based, nondeterministic programming language for solving graph problems at a high level of abstraction, freeing programmers from dealing with low-level data structures. In this case study, we present a graph program which minimizes finite automata. The program represents an automaton by its transition diagram, computes the state equivalence relation, and merges...

Constraint automata have been used as an operational model for Reo which offers a channel-based framework to compose complex component connectors. In this paper, we introduce a variant of constraint automata with discrete probabilities and nondeterminism, called probabilistic constraint automata. These can serve for compositional reasoning about connector components, modelled by Reo circuits wi...

Given a language L and a nondeterministic finite automaton M , we consider whether we can determine efficiently (in the size of M) if M accepts at least one word in L, or infinitely many words. Given thatM accepts at least one word in L, we consider how long the shortest word can be. The languages L that we examine include the palindromes, the nonpalindromes, the k-powers, the non-k-powers, the...

The aim of this paper is to compare three efficient representations of the position automaton of a regular expression: the Thompson εautomaton, the ZPC-structure and the F-structure, an optimization of the ZPC-structure. These representations are linear w.r.t. the size s of the expression, since their construction is in O(s) space and time, as well as the computation of the set δ(X, a) of the t...

We study the strength of axioms needed to prove various results related to automata on infinite words and Büchi’s theorem on the decidability of the MSO theory of (N,≤). We prove that the following are equivalent over the weak second-order arithmetic theory RCA0: 1. Büchi’s complementation theorem for nondeterministic automata on infinite words, 2. the decidability of the depth-n fragment of th...