In the context of a compositional theory of automata [8] (CP automata) we define a notion of hierarchical automaton, and show how the P-systems of Gh. Păun [9] may be described in terms of these automata. A distributive law for CP automata is proved which relates two different views of hierarchical systems: the first view is that hierarchical systems consist of layers, with communication betwee...

Along with the usual predicates “prefix” and “equal length”, the predicate “equal last letter” leads to a first order theory of the free infinitely generated monoid whose definable relations are related to the algebra of relations recognized by different types of multitape automata which are natural extensions of the famous Rabin-Scott multitape automata and the so-called synchronous automata. ...

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...

We show how to use duality theory to construct minimized versions of a wide class of automata. We work out three cases in detail: (a variant of) ordinary automata, weighted automata and probabilistic automata. The basic idea is that instead of constructing a maximal quotient we go to the dual and look for a minimal subalgebra and then return to the original category. Duality ensures that the mi...

We consider the family of rational relations on words, i.e., relations recognized by multitape automata, which have rational trace on any finite intersection of rational relations. We prove that this family consists of finite unions of relations which are of two types: stars of tuples possibly with an extra prefix and suffix and relations with all but one singleton set components.

This article studies the expressive power of finite automata recognizing sets of real numbers encoded in positional notation. We consider Muller automata as well as the restricted class of weak deterministic automata, used as symbolic set representations in actual applications. In previous work, it has been established that the sets of numbers that are recognizable by weak deterministic automat...

A novel approach to automata-based modeling for spatial systems is described: geographic automata and Geographic Automata Systems. We detail a framework that takes advantage of the formalism of automata theory and GI Science to unite cellular automata and multi-agent systems techniques, and provides a spatial approach to bottom-up modeling of complex geographic systems that are comprised of inf...

We start by introducing a notion of hybrid automata with a clear identiication of the signature component. Hybrid automata intermix discrete and continuous behavior, extending non-deterministic automata with attributes that evolve continuously with time according to evolution laws. Adopting a categorial approach to aggregating and interconnecting hybrid automata we look at a suitable deenition ...

In this paper, we define a new class of combined automata, called temporalized automata, which can be viewed as the automata-theoretic counterpart of temporalized logics, and show that relevant properties, such as closure under Boolean operations, decidability, and expressive equivalence with respect to temporal logics, transfer from component automata to temporalized ones. Furthermore, we succ...

Automata for unranked trees form a foundation for XML schemas, querying and pattern languages. We study the problem of efficiently minimizing such automata. We start with the unranked tree automata (UTAs) that are standard in database theory, assuming bottomup determinism and that horizontal recursion is represented by deterministic finite automata. We show that minimal UTAs in that class are n...