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...

Enumerating regular expressions and their languages p. 2 A general weighted grammar library p. 23 On the complexity of Hopcroft's state minimization algorithm p. 35 Implementation of catalytic P systems p. 45 Code selection by tree series transducers p. 57 Some non-semi-decidability problems for linear and deterministic context-free languages p. 68 Brute force determinization of NFAs by means o...

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...

The classical Tarski theorem on topological semantics of modal logic states that the logic S4 is complete in R for each n. Recently several authors have considered logics of dynamic topological systems, which is a topological space and a function on it. In [1] a bimodal logic S4C was introduced and proven to be complete with respect to the class of all continuous dynamic systems. A number of po...

The classical Tarski theorem on topological semantics of modal logic states that the logic S4 is complete in R for each n. Recently several authors have considered logics of dynamic topological systems, which is a topological space and a function on it. In [1] a bimodal logic S4C was introduced and proven to be complete with respect to the class of all continuous dynamic systems. A number of po...

Proof. Myhill has proved that any productive set is productive under a 1-1 total function. A corresponding result is easily established for any contraproductive set having at least one total contraproductive function. Letting h(x, y) be the recursive function of [2, Theorem 2.4, p. 69], consider the sequence s0 = h(0, 0), Sx — h(l, s0), s2 = h(0, Sx), Si = h(i, s2), Si = h(2, S3), and so on. Th...

In this technical report we describe a general class of monoids for which (sub)sequential rational can be characterised in terms of a congruence relation in the flavour of Myhill-Nerode relation. The class of monoids that we consider can be described in terms of natural algebraic axioms, contains the free monoids, groups, the tropical monoid, and is closed under Cartesian. 1 Inroduction The pro...

Let T be the set of ground terms over a nite ranked alphabet We de ne partial automata on T and prove that the nitely gener ated congruences on T are in one to one correspondence up to iso morphism with the nite partial automata on T with no inaccessible and no inessential states We give an application in term rewriting every ground term rewrite system has a canonical equivalent system that can...

Cayley graphs considered as language recognisers are as powerful as the more general finite state automata. This paper applies Cayley graphs to define a class of automata and describe minimal automata of this type, all their congruences and the Nerode equivalence of states. Throughout, the word graph means a finite directed graph without multiple edges but possibly with loops, and D = (V,E) is ...

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...