Recently, a characterization of the class of nondeterministic finite automata (NFAs) for which determinization results in a minimal deterministic finite automaton (DFA), was given in [2]. We present a similar result for the case of symmetric difference NFAs. Also, we show that determinization of any minimal symmetric difference NFA produces a minimal DFA.

We investigate a subclass of languages recognized by vector addition systems, namely languages of nondeterministic Parikh automata. While the regularity problem (is the language of a given automaton regular?) is undecidable for this model, we show surprising decidability of the regular separability problem: given two Parikh automata, is there a regular language that contains one of them and is ...

Counter automata are more powerful versions of finitestate automata where addition and subtraction operations are permitted on a set of n integer registers, called counters. We show that the word problem of Z is accepted by a nondeterministic m-counter automaton if and only if m ≥ n.

We adapt direct, delayed, and fair simulation to alternating Büchi automata. Unlike with nondeterministic Büchi automata, naive quotients do not preserve the recognized language. As a remedy, we present specifically designed definitions of quotients, namely minimax and semi-elective quotients: minimax quotients, which are simple and have a minimum number of transitions, preserve the recognized ...

We present a reinterpretation of the Kameda-Weiner method of finding a minimal nondeterministic finite automaton (NFA) of a language, in terms of atoms of the language. We introduce a method to generate NFAs from a set of languages, and show that the Kameda-Weiner method is a special case of it. Our method provides a unified view of the construction of several known NFAs, including the canonica...

An ω-categorical supersimple group is finite-by-abelian-by-finite, and has finite SU -rank. Every definable subgroup is commensurable with an acl(∅)definable subgroup. Every finitely based regular type in a CM-trivial ω-categorical simple theory is non-orthogonal to a type of SU -rank 1. In particular, a supersimple ω-categorical CM-trivial theory has finite SU -rank.

To prove Theorem 2, we use the following two facts about the class F: 1. F is a differential ring [2]. This means that F is closed under addition, multiplication and differentiation. 2. All functions y ∈ F are entire functions of completely regular growth in the sense of Levin–Pflüger [4], with piecewise-trigonometric indicators, the notions which we recall now. Let f be a holomorphic function ...

A sweeping automaton is a two-way deterministic finite automaton which makes turns only at the endmarkers. Sipser [12] has proved that one-way nondeterministic finite automata can be exponentially more succinct in sizes than sweeping automata. In this paper, we propose a technique based on the work in [6] for establishing lower bounds on the size of sweeping automata. We show that Sipser’s tech...

We resolve an open problem raised by Ravikumar and Ibarra [SIAM J. Comput., 18 (1989), pp. 1263–1282] on the succinctness of representations relating to the types of ambiguity of finite automata. We show that there exists a family of nondeterministic finite automata {An} over a two-letter alphabet such that, for any positive integer n, An is exponentially ambiguous and has n states, whereas the...