In this paper we study the problem of minimising deterministic automata over finite and infinite words. Deterministic finite automata are the simplest devices to recognise regular languages, and deterministic Büchi, Co-Büchi, and parity automata play a similar role in the recognition of ω-regular languages. While it is well known that the minimisation of deterministic finite and weak automata i...

In this paper, we define the notion of biRFSA which is a residual finate state automaton (RFSA) whose the reverse is also an RFSA. The languages recognized by such automata are called biRFSA languages. We prove that the canonical RFSA of a biRFSA language is a minimal NFA for this language and that each minimal NFA for this language is a sub-automaton of the canonical RFSA. This leads to a char...

In this report we study the problem of minimising deterministic automata over finite and infinite words. Deterministic finite automata are the simplest devices to recognise regular languages, and deterministic Büchi, Co-Büchi, and parity automata play a similar role in the recognition of ω-regular languages. While it is well known that the minimisation of deterministic finite and weak automata ...

This paper is devoted to the study of nondeterministic closure automata, that is, nondeterministic finite automata (nfas) equipped with a strict closure operator on the set of states and continuous transition structure. We prove that for each regular language L there is a unique minimal nondeterministic closure automaton whose underlying nfa accepts L. Here minimality means no proper sub or quo...

We consider weighted o-minimal hybrid systems, which extend classical o-minimal hybrid systems with cost functions. These cost functions are “observer variables” which increase while the system evolves but do not constrain the behaviour of the system. In this paper, we prove two main results: (i) optimal o-minimal hybrid games are decidable; (ii) the model-checking of WCTL, an extension of CTL ...

We consider weighted o-minimal hybrid systems, which extend classical o-minimal hybrid systems with cost functions. These cost functions are “observer variables” which increase while the system evolves but do not constrain the behaviour of the system. In this paper, we prove two main results: (i) optimal o-minimal hybrid games are decidable; (ii) the model-checking of WCTL, an extension of CTL ...

Over the last decades the theory of automata on infinite objects has been an important source of tools for the specification and the verification of computer programs. Trees are more suitable than words to model nondeterminism and concurrency. In the literature, there are several examples of acceptance conditions that have been proposed for automata on infinite words and then have been fruitful...

Symbolic finite automata extend classical automata by allowing infinite alphabets given by Boolean algebras and having transitions labeled by predicates over such algebras. Symbolic automata have been intensively studied recently and they have proven useful in several applications. We study some theoretical aspects of symbolic automata. Especially, we study minterms of symbolic automata, that i...

We propose the characterization of binary cellular automata using a set of behavioral metrics that are applied to the minimal Boolean form of a cellular automaton’s transition function. These behavioral metrics are formulated to satisfy heuristic criteria derived from elementary cellular automata. Behaviors characterized through these metrics are growth, decrease, chaoticity, and stability. Fro...

We study congruences on words in order to characterize the class of visibly pushdown languages (VPL), a subclass of context-free languages. For any language L, we define a natural congruence on words that resembles the syntactic congruence for regular languages such that this congruence is of finite index if, and only if, L is a VPL. We then study the problem of finding canonical minimal determ...