In this paper, a reflection is made on an indeterminism inherent to Hopcroft’s minimization algorithm: the splitter choice. We have implemented two natural policies (FIFO and FILO) for managing the set of splitters for which we obtain the following practical results: the FILO strategy performs better than the FIFO strategy, in the case of a one letter alphabet, the practical complexity in the F...

In this work, we give an algorithm that infers Regular Trace Languages. Trace languages can be seen as regular languages that are closed under a partial commutation relation called the independence relation. This algorithm is similar to the RPNI algorithm, but it is based on Asynchronous Cellular Automata. For this purpose, we define Asynchronous Cellular Moore Machines and implement the merge ...

Multirate timed automata 2] are an extension of timed automata 3] where each clock has its own speed varying between a lower and an upper bound that may change from one control location to another. This formalism is well-suited for specifying hybrid systems where the dynamics of the continuous variables are deened or can be approximated by giving the minimal and maximal rate of change. To avoid...

Abstract. For applications to cryptography, it is important to represent numbers with a small number of non-zero digits (Hamming weight) or with small absolute sum of digits. The problem of finding representations with minimal weight has been solved for integer bases, e.g. by the non-adjacent form in base 2. In this paper, we consider numeration systems with respect to real bases β which are Pi...

We continue investigation of languages, accepted by timed automata of Alur and Dill. In [ACM97] timed regular expressions equivalent to timed automata were introduced. Here we introduce quasilinear equations over timed languages with regular coefficients. We prove that the minimal solution of such an equation is regular and give an algorithm to calculate this solution. This result is used to ob...

Fuzzy Finite Tree Automata (FFTA) are natural generalizations of fuzzy automata on words. FFTA accept fuzzy tree languages and are used in many areas of mathematics, computer science and engineering. Therefore, it is important to design algorithms that reduce the size (number of states) of automata, and find the minimal FFTA that recognizes the same language as a given FFTA. We present two mini...

Determinisation of nondeterministic finite automata is a well-studied problem that plays an important role in compiler theory and system verification. In the latter field, one often encounters automata consisting of millions or even billions of states. On such input, the memory usage of analysis tools becomes the major bottleneck. In this paper we present several determinisation algorithms, all...

Recently testing of Quantum-dot Cellular Automata (QCA) Circuits has attracted a lot of attention. In this paper, QCA is investigated for testable implementations of reversible logic. To amplify testability in Reversible QCA circuits, a test method regarding to Built In Self Test technique is developed for detecting all simulated defects. A new Reversible QCA MUX 2×1 desig...

The present paper uses spectral theory of linear operators to construct approximately minimal realizations of weighted languages. Our new contributions are: (i) a new algorithm for the SVD decomposition of infinite Hankel matrices based on their representation in terms of weighted automata, (ii) a new canonical form for weighted automata arising from the SVD of its corresponding Hankel matrix a...

In this paper we introduce the notion of merging states and merging systems and we use it for the classification of finite deterministic automata without initial and final states. We investigate the dependencies between the structure of an automaton described by merging systems and maximal lengths of minimal synchronizing words for automata which structures belong to the given class of merging ...