A pattern is encountered in a word if some infix of the word is the image of the pattern under some non-erasing morphism. A pattern p is unavoidable if, over every finite alphabet, every sufficiently long word encounters p. A theorem by Zimin and independently by Bean, Ehrenfeucht and McNulty states that a pattern over n distinct variables is unavoidable if, and only if, p itself is encountered...

We show that the solution published in the paper by Senovilla [Phys. Rev. Lett. 64, 2219 (1990)] is geodesically complete and singularity-free. We also prove that the solution satisfies the stronger energy and causality conditions, such as global hyperbolicity, the strong energy condition, causal symmetry, and causal stability. A detailed discussion about which assumptions in the singularity th...

Contemporary living conditions impose the need for optimum responses. Hence, the purpose of Kinesiology as a science should be to serve the society, nation and civilisation. The issue of free time and its contents is one of the central issues set before a modern man. The prospect of its design can be found in education as the main precondition for creating a habit of active use of free time. Ki...

A randomised polylog time algorithm is given for deciding whether or not the sets of words of a given length generated by two unam-biguous context-free grammars coincide. The algorithm is in randomised NC4 in terms of the product of the grammar size and the length.

Ellul, Krawetz, Shallit and Wang prove an exponential lower bound on the size of any context-free grammar generating the language of all permutations over some alphabet. We generalize their method and obtain exponential lower bounds for many other languages, among them the set of all squares of given length, and the set of all words containing each symbol at most twice.

A graph is called t-perfect if its stable set polytope is defined by nonnegativity, edge and odd-cycle inequalities. We show that it can be decided in polynomial time whether a given claw-free graph is t-perfect.

We study the compressed word problem: a variant of the word problem for finitely generated groups where the input word is given by a context-free grammar that generates exactly one string. We show that finite extensions and free products preserve the complexity of the compressed word problem. Also, the compressed word problem for a graph group can be solved in polynomial time. These results all...

In this paper we describe a method of translating a Lambek grammar with one division into an equivalent context-free grammar whose size is bounded by a polynom from the size of the original grammar. Earlier constructions by Buszkowski and Pentus lead to exponential growth of the grammar size. 1 Lambek Grammars and Context-Free Gram-