We show that the absolute worst case time complexity for Hopcroft’s minimization algorithm applied to unary languages is reached only for deterministic automata or cover automata following the structure of the de Bruijn words. A previous paper by Berstel and Carton gave the example of de Bruijn words as a language that requires O(n log n) steps in the case of deterministic automata by carefully...

This theory defines deterministic and nondeterministic automata in a functional representation: the transition function/relation and the finality predicate are just functions. Hence the state space may be infinite. It is shown how to convert regular expressions into such automata. A scanner (generator) is implemented with the help of functional automata: the scanner chops the input up into long...

Parsing with finite automata networks implies, in one way, the conversion of a regular expression into a minimal deterministic finite automaton, while parsing with neural networks involves parsing of a natural language sentence. In ‘Parsing with finite automata networks’ finite automata are frequently combined using a set of rules for various operations like union, concatenation, and kleene clo...

Automata over infinite words provide a powerful framework, which we can use to solve various decision problems. However, the automatized reasoning with restricted classes of automata over infinite words is often simpler and more efficient. For instance, weak deterministic Büchi automata, which recognize the ω-regular languages in the Borel class Fσ ∩Gδ, can be handled algorithmically almost as ...

We provide a Kleene Theorem for (Rabin) probabilistic automata over finite words. Probabilistic automata generalize deterministic finite automata and assign to a word an acceptance probability. We provide probabilistic expressions with probabilistic choice, guarded choice, concatenation, and a star operator. We prove that probabilistic expressions and probabilistic automata are expressively equ...

Watson–Crick automata are finite state automata working on double-stranded tapes, introduced to investigate the potential of DNA molecules for computing. In this paper, we continue the investigation of descriptional complexity ofWatson–Crick automata initiated by Păun et al. [A. Păun, M. Păun, State and transition complexity of Watson–Crick finite automata, in: G. Ciobanu, G. Paun (Eds.), Funda...

We give a canonical representation for minimal acyclic deterministic finite automata (MADFA) with n states over an alphabet of k symbols. Using this normal form, we present a method for the exact generation of MADFAs. This method avoids a rejection phase, that would be needed if a generation algorithm for a larger class of objects that contains the MADFAs were used. We give an upper bound for M...

We survey in this paper some variants of the notion of determinism, refining the spectrum between non-determinism and determinism. We present unambiguous automata, strongly unambiguous automata, prophetic automata, guidable automata, and history-deterministic automata. We instantiate these various notions for finite words, infinite words, finite trees, infinite trees, data languages, and cost f...

This paper gives answers to questions formulated as open in the paper “On State Observability in Deterministic Finite Automata” by A. Mateescu and Gh. Păun. Specifically, it demonstrates that for all k ≥ 2, the families of regular languages acceptable by deterministic finite automata with no more than k semiobservable states, denoted by Tk, are anti-AFL’s, and that the family T1 differs in the ...

Finite automata are one of the oldest and most intensely investigated computational models. Historically, the theory of finite automata counts among the oldest topics in computer science, and is one of the basic building blocks of the theory of formal languages. Its origins can be tracked back to the 1940’s, when finite automata were used to model nerve nets [6]. Since its original discovery, f...