The synchronization problem for a deterministic n-state automaton consists in the search of an input-sequence, called a synchronizing word such that the state attained by the automaton, when this sequence is read, does not depend on the initial state of the automaton itself. If such a sequence exists, the automaton is called synchronizing. If the automaton is deterministic and complete, a well-...

This paper presents an efficient algorithm for the incremental construction of a minimal acyclic sequential transducer (ST) for a dictionary consisting of a list of input and output strings. The algorithm generalises a known method of constructing minimal finite-state automata (Daciuk et al., 2000). Unlike the algorithm published by Mihov and Maurel (2001), it does not require the input strings...

State minimization plays a fundamental role in both classical automata theory and in the theory of reactive systems. Many algorithms and results are based on the fact that for each nite automaton there exists an equivalent minimum state automaton that can be eeectively computed and that is unique up to isomorphism. Timed safety automata (TSA's) 5], nite automata with clocks, have been used exte...

In this paper we compare the architecture of early computing devices trying to understand if they contain the minimal structure needed to qualify as universal computers. Our intention is to bring some order into the discussion about the inventor or inventors of the computer by adopting a clear cut definition of such devices. We consider the minimal structure and the minimal instruction set comp...

These notes report on recent advances in the relatively new area of hyper-minimization. Several open questions that were raised in the pioneering article [Badr, Geffert, and Shipman. Hyper-minimizing minimized deterministic finite state automata. RAIRO Theor. Inf. Appl., 43(1):69–94, 2009] are addressed here and the solutions, which are mostly taken from the literature, are presented in a unifo...

The minimal deterministic finite automaton is generally used to determine regular languages equality. Antimirov and Mosses proposed a rewrite system for deciding regular expressions equivalence of which Almeida et al. presented an improved variant. Hopcroft and Karp proposed an almost linear algorithm for testing the equivalence of two deterministic finite automata that avoids minimisation. In ...

This paper is a follow-up to Jan Daciuk’s experiments on space-efficient finite state automata representation that can be used directly for traversals in main memory [4]. We investigate several techniques of reducing the memory footprint of minimal automata, mainly exploiting the fact that transition labels and transition pointer offset values are not evenly distributed and so are suitable for ...

The 1984 article by Martin, Odlyzko and Wolfram on Wolfram’s Rule 90 heightened interest in the area of linear cellular automata defined on a vector space over a finite field [8]. In this article we find the closed form expression for the minimal polynomial of Rule 90, which is then used to completely characterize the dynamics of the map. In addition, we show that the standard basis vectors in ...

The problem of efficiently minimizing deterministic weighted tree automata (wta) is investigated. Such automata have found promising applications as language models in Natural Language Processing. A polynomial-time algorithm is presented that given a deterministic wta over a commutative semifield, of which all operations including the computation of the inverses are polynomial, constructs an eq...