We present two results which shed some more light on the deep connection between ZFA and the standard ZF set theory: First of all we refine a result of Forti and Honsell (see [5]) in order to prove that the universe of ZFA can also be obtained (without appealing to choice) as the least fixed point of a continuous operator and not only as the greatest fixed point of the powerset operator. Next w...

We show how to calculate the maximum number of edits per character needed to convert any string in one regular language to a string in another language. Our algorithm makes use of a local determinization procedure applicable to a subclass of distance automata. We then show how to calculate the same property when the editing needs to be done in streaming fashion, by a finite state transducer, us...

The article defines and studies the genus of finite state deterministic automata (FSA) and regular languages. Indeed, a FSA can be seen as a graph for which the notion of genus arises. At the same time, a FSA has a semantics via its underlying language. It is then natural to make a connection between the languages and the notion of genus. After we introduce and justify the the notion of the gen...

In this paper we combine determinization and state reduction methods into two-in-one algorithms that simultaneously perform determinization and state reduction. These algorithms perform better than all previous determinization algorithms for fuzzy finite automata, developed by Bělohlávek [Inform Sciences 143 (2002) 205–209], Li and Pedrycz [Fuzzy Set Syst 156 (2005) 68–92], Ignjatović et al. [I...

Complementation and determinization are two fundamental notions in automata theory. The close relationship between the two has been well observed in the literature. In the case of nondeterministic finite automata on finite words (NFA), complementation and determinization have the same state complexity, namely Θ(2n) where n is the state size. The same similarity between determinization and compl...

In this paper, we develop the basic theory of disimulations, a type of relation between two automata which witnesses equivalence. We show that many standard constructions in the theory of automata such as determinization, minimization, inaccessible state removal, et al., are instances of disimilar automata. Then, using disimulations, we define an “algebraic” proof system for the equational theo...

We present a sound and complete axiomatization of finite complete trace semantics for generative probabilistic transition systems. Our approach is coalgebraic, which opens the door to axiomatize other types of systems. In order to prove soundness and completeness, we employ determinization and show that coalgebraic traces can be recovered via determinization, a result interesting in itself. The...

In the automata-theoretic approach to verification, we translate specifications to automata. Complexity considerations motivate the distinction between different types of automata. Already in the 60’s, it was known that deterministic Büchi word automata are less expressive than nondeterministic Büchi word automata. The proof is easy and can be stated in a few lines. In the late 60’s, Rabin prov...

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.

In this paper we establish a lower bound hist(n) for the problem of translating a Büchi word automaton of size n into a deterministic Rabin word automaton when both the Büchi and the Rabin condition label transitions rather than states. This lower bound exactly matches the known upper bound to this problem. The function hist(n) is in Ω((1.64n)) and in o((1.65n)). Our result entails a lower boun...