Tree automata and logic programs

Abstract

Each clause of a definite sentence can be read as a move of a tree automaton. These tree automata, called pattern replacing automata (PRA), are introduced and studied in this paper.

The tree languages accepted by PRA are (very close to) the minimal Herbrand models of definite sentences. Moreover, PRA are quite natural automata : they can be viewed as a natural extension of top-down tree automata. Thus, by means of PRA, one can make use of well-known techniques and ideas of automata theory for studying definite sentences. As a proof of this fact, mainly using simulation techniques classical in automata theory, we give constructive proofs that :

• (a) Each PRA (and hence each definite sentence) can be put into particularly simple forms ; for definite sentences these special forms are as follows : (1) in each clause the premise contains all the variables of the conclusion ; (2) in each clause all variables of the premise appear also in the conclusion ; and (3) in each clause the height of the terms of the premise is one at most and the height of the terms of the conclusion is two at most.

• (b) The class of tree languages recognized by a restricted class of PRA, called monadic weak PRA, coincides with the class of recognizable tree languages.

The rest of the paper consists of two sections. In section 1 we shortly give the necessary definitions and in section 2 we intuitively explain the results mentioned above.