Degrees of Free Word-Order and Freely Rewriting Restarting Automata

In natural languages with a high degree of word-order freedom syntactic phenomena like dependencies (subordinations) or valencies do not depend on the word-order (or on the individual positions of the individual words). This means that some permutations of sentences of these languages are in some (important) sense syntactically equivalent. Here we study this phenomenon in a formal way. Various types of j-monotonicity for restarting automata can serve as parameters for the degree of word-order freedom and for the complexity of word-order in sentences (languages). Here we combine two types of parameters on computations of restarting automata: 1. the degree of j-monotonicity, and 2. the number of rewrites per cycle. We study these notions formally in order to obtain an adequate tool for modelling and comparing formal descriptions of (natural) languages with different degrees of word-order freedom and word-order complexity.

The Degree of Word-Expansion of Lexicalized RRWW-Automata

Restarting automata can be seen as analytical variants of classical automata as well as of regulated rewriting systems. We study a measure for the degree of nondeterminism of (context-free) languages in terms of deterministic restarting automata that are (strongly) lexicalized. This measure is based on the number of auxiliary symbols (categories) used for recognizing a language as the projection of its characteristic language onto its input alphabet. This type of recognition is typical for analysis by reduction, a method used in linguistics for the creation and verification of formal descriptions of natural languages. Our main results establish a hierarchy of classes of context-free languages and two hierarchies of classes of non-context-free languages that are based on the expansion factor of a language.