In this technical report we describe a general class of monoids for which (sub)sequential rational can be characterised in terms of a congruence relation in the flavour of Myhill-Nerode relation. The class of monoids that we consider can be described in terms of natural algebraic axioms, contains the free monoids, groups, the tropical monoid, and is closed under Cartesian. 1 Inroduction The pro...

Cayley graphs considered as language recognisers are as powerful as the more general finite state automata. This paper applies Cayley graphs to define a class of automata and describe minimal automata of this type, all their congruences and the Nerode equivalence of states. Throughout, the word graph means a finite directed graph without multiple edges but possibly with loops, and D = (V,E) is ...

Tree transducers are an expressive formalism for reasoning about tree structured data. Practical applications range from XSLT-like document transformations to translations of natural languages. Important problems for transducers are to decide whether two transducers are equivalent, to construct normal forms, give semantic characterizations, and type checking, i.e., to check whether the produced...

Advances in t,he theory of well-partially-ordered sets now make it possible to prove the existence of low-degree polynomial-time decision algorithms for a vast assortment of natural problems, many of which seem to resist more traditional means of complexity classification. Surprisingly, these proofs are nonconstructive, based on the promise of an iiiiknown but finite obstruction set. Recent pro...

The NuPRL system [3] was designed for interactive writing of machine–checked constructive proofs and for extracting algorithms from the proofs. The extracted algorithms are guaranteed to be correct 1 which makes it possible to use NuPRL as a programming language with built-in verification[1,5,7,8,9,10]. However it turned out that proofs written without algorithmic efficiency in mind often produ...

We consider the notion of rationality in algebras with a designated binary associative operation called the series operation, or the sequential product. We define automata operating in these algebras and rational expressions matching their expressive power, and we show that this expressive power equals that of algebraic recognizability. The framework which we consider encompasses both the free ...

We present a constructive formalization of the Myhill-Nerode theorem on the minimization of nite automata that follows the account in Hopcroft and Ullman's book Formal Languages and Their Relation to Automata. We chose to formalize this theorem because it illustrates many points critical to formalization of computational mathematics, especially the extraction of an important algorithm from a pr...

Finite automata have been recently used as alternative, discrete models in theoretical physics, especially in problems related to the dichotomy between endophysical/intrinsic and exophysical/extrinsic perception (see, for instance [15, 18, 16, 7, 17, 4]). These studies deal with Moore experiments; the main result states that it is impossible to determine the initial state of an automaton, and, ...

We present a novel canonical automaton model, based on register automata, that can be used to specify protocol or program behavior. Register automata have a finite control structure and a finite number of registers (variables), and process sequences of terms that carry data values from an infinite domain. We consider register automata that compare data values for equality. A major contribution ...

In this paper, we establish the concept of regularity for languages consisting of Message Sequence Charts (MSCs). To this aim, we formalise their behaviour by string languages and give a natural definition of regularity in terms of an appropriate Nerode right congruence. Moreover, we present a class of accepting automata and, using this characterisation, establish several decidability and closu...