Finite-Word Hyperlanguages

A Finite Word Poset

Our word posets have finite words of bounded length as their elements, with the words composed from a finite alphabet. Their partial ordering follows from the inclusion of a word as a subsequence of another word. The elemental combinatorial properties of such posets are established. Their automorphism groups are determined (along with similar result for the word poset studied by Burosch, Frank ...

Word Values in Finite Groups

Let w = w(x1, ..., xd) denote a group word in d variables, that is, an element of the free group of rank d. For a finite group G we may define a word map that sends a d-tuple, (g1, ..., gd) of elements of G, to its w-value, w(g1, ..., gd), by substituting variables and evaluating the word in G by performing all relevant group operations. In this thesis we study a number of problems to do with t...

Extending word problems in deterministic finite automata

A word w is extending a subset of states S of a deterministic finite automaton, if the set of states mapped to S by w (the preimage of S under the action of w) is larger than S. This notion together with its variations has particular importance in the field of synchronizing automata, where a number of methods and algorithms rely on finding (short) extending words. In this paper we study the com...

Finite Moniods: From Word to Circuit Evaluation

Finite Automata for Processing Word Order

This paper is concerned with applications of-nite state automata (FSA) to word order processing. As the surface order of constituents is a function of many interacting factors, an adequate formalisation seems fairly complicated. I argue that despite this complexity, most ordering constraints observed in free word order languages can be treated by lower-level methods such as nite state automata....