The automated inference of tree system

Tree systems are used in syntactic pattern recognition for describing two-dimensional patterns. We extend results on tree automata with the introduction of the subtree-invariant equivalence relation R. R relates two trees when the appearance of one implies the appearance of the other in similar trees. A new state minimizing algorithm for tree automata is formed using R. We also determine a bound for Brainerd's minimization method. We introduce the Group Unordered Tree Automaton (GUTA) which accepts all orientations of open-line patterns described using directed arc primitives. The specification of a GUTA includes an unordered tree automaton M, which only accepts a standard orientation of a given class of open-line pictures, and a transformation group, which describes how the primitives transform under rotational shifts. The GUTA performs all orientational parses in parallel, reports all successful transformations and operates in the same time complexity as M. The GUTA is much easier to specify than the equivalent non-decomposed unordered tree automaton. The problem of automating the design of unordered and ordered tree automata (grammars) is studied both on a system directed and on a highly interactive level. The system directed method uses Pao's lattice technique to infer tree automata (grammars) from structurally complete samples. It is shown that the method can infer any context-free grammar when provided with skeletal structure descriptions. This extends the results of Pao which only deal with proper subclasses of context-free grammars. The highly interactive inference system is based on the use of tree derivatives, also introduced in this thesis, for determining automaton states and possible state merging. Tree derivatives are sets of tree forms derived by replacing selected subtrees with marked nodes. The derivative sets are used to determine subtree-invariant equivalence relations which characterize tree automata. A minimization algorithm based on tree derivatives is given. We use tree derivatives to prove that a tree automaton with n states can be fully characterized by the set of trees that it accepts of depth at most 2n. The inference method compares tree derivative sets and infers subtree-invariant equivalence relations. A relation is inferred if there is sufficient overlap between the derivative sets. Our method was compared to other tree automata inference schemes, including Crespi-Reghizzi's algorithm. We have shown that our method is applicable to the entire class of context-free grammars and requires a smaller sample than Crespi-Reghizzi's algorithm which can only infer a proper subclass of operator precedence grammars. Furthermore, it appears more general than the other inference systems for tree automata or grammars

Nondeterministic Moore automata and Brzozowski's minimization algorithm

Moore automata represent a model that has many applications. In this paper we define a notion of coherent nondeterministic Moore automaton (NMA) and show that such a model has the same computational power of the classical deterministic Moore automaton. We consider also the problem of constructing the minimal deterministic Moore automaton equivalent to a given NMA. We propose an algorithm that is a variant of Brzozowski’s minimization algorithm in the sense that it is essentially structured as reverse operation and subset construction performed twice. Moreover, we explore more general classes of NMA and analyze the applicability of the algorithm. For some of such classes the algorithm does not return the minimal equivalent deterministic automaton