In this workwe shall consider a notion of complexity of formal languages L that is inspired by the concept of entropy from dynamical systems. More precisely, we shall define the topological entropy of L to be the exponential growth-rate of the restrictions of the Nerode congruence relation of L to words of length at most n. We shall show that the topological entropy of regular languages is alwa...

Motivation Minimizing deterministic automata −→ Merging states with the same future a b a a b b (Nerode equivalence) −→ Hopcroft algorithm O(n log n) Motivation Minimizing deterministic automata −→ Merging states with the same future a b a a b b (Nerode equivalence) −→ Hopcroft algorithm O(n log n)

1 Introduction ✤ Just as there is the Russell paradox about sets, so there is the Russell-Myhill paradox of propositions. ✤ While predicativity has been well-explored as a response to the Russell paradox of sets, there seems to have been no previous attempt to set out a predicative solution to the Russell-Myhill paradox of propositions. ✤ The aim of this talk is to do that, within the framework...

We shall discuss a variety of results on Answer Set Programming based on the work of author with Marek, Nerode, Blair and Cenzer that have arisen by looking at Answer Set Programming from a mathematical perspective. This includes work with Nerode and Marek (Marek, Nerode, & Remmel 1990; 1992c; 1992b; 1992a; 1994; 1997; 1999) Nonmonotonic Proof Systems which allows one to gives a common generali...

This thesis presents new techniques for the construction and specification of linear tail-biting trellises. Tail-biting trellises for linear block codes are combinatorial descriptions in the form of layered graphs, that are somewhat more compact than the corresponding conventional trellis descriptions. Conventional trellises for block codes have a well understood underlying theory. On the other...

Hyperedge replacement grammars (HRGs, see [7, 6]) are one of the most successful formal models for the generative specification of graph languages, thanks to the fact that their language-theoretic and algorithmic properties to a great extent resemble those of contextfree grammars. Unfortunately, polynomial parsing is an exception from this general rule: graph languages generated by HRGs may be ...

both the branching factor and the computation time for the systems based on LG were several times smaller than those for the competition (Stilman, 1994a). Note that although LG has a discrete nature, it has been applied to some continuous systems as well through an ad hoc discretization of the latter (Stilman, 19941995). The Linguistic Geometry (LG) approach to discrete systems was introduced B...