By the Myhill-Nerode Theorem, a tree language L is recognisable if and only if ≡L has finite index. The minimal bottom-up DFTA of L is then defined using the congruence classes of ≡L as states. Exercise 1 (Bottom-up Residuals). Let L ⊆ T (F) and t ∈ T (F). The bottom-up residual of L by t is the set of all contexts C such that C[t] ∈ L: t−1L def = {C ∈ C(F) | C[t] ∈ L} . 1. Show that L is recog...

We consider several aspects of Wilke’s [T. Wilke, An algebraic characterization of frontier testable tree languages, Theoret. Comput. Sci. 154 (1996) 85–106] tree algebra formalism for representing binary labelled trees and compare it with approaches that represent trees as terms in the traditional way. A convergent term rewriting system yields normal form representations of binary trees and co...

In this paper, we explore the appli ability to ompression tasks of the algorithms for regular language inferen e from sto hasti samples. We ompare two arithmeti en oders based upon two di erent kinds of formal languages: string languages and tree languages. The experiments show that tree-based methods outperform the predi tive apability of stringbased methods when they are applied to les ontain...

Fuzzy Decision Tree induction is a powerful methodology to extract human interpretable classification rules. The induction of fuzzy decision tree is done using popular Fuzzy ID3 algorithm [1, 2]. The other parameters which influence the performance of fuzzy decision tree are cut standard parameter  and leaf selection threshold parameter th  . Generally these parameters are to be selected heur...

Fuzzy automata have long been accepted as a generalization of nondeterministic finite automata. A closer examination, however, shows that the fundamental property—nondeterminism—in nondeterministic finite automata has not been well embodied in the generalization. In this paper, we introduce nondeterministic fuzzy automata with or without -moves and fuzzy languages recognized by them. Furthermor...

A fuzzy logic based resource manager (RM) that will allocate resources distributed across many platforms is under development. The platforms will consist of ships, aircraft, etc. The resources will be various sensors: ESM, RADAR, IFF, and communications. The RM will allow codification of military expertise in a simple mathematical formalism known as the fuzzy decision tree. The fuzzy decision t...