The compressed word problem for a finitely generated monoid M asks whether two given compressed words over the generators of M represent the same element of M . For string compression, straight-line programs, i.e., contextfree grammars that generate a single string, are used in this paper. It is shown that the compressed word problem for a free inverse monoid of finite rank at least two is comp...

Post Embedding Problems are a family of decision problems based on the interaction of a rational relation with the subword embedding ordering, and are used in the literature to prove non multiply-recursive complexity lower bounds. We refine the construction of Chambart and Schnoebelen (LICS 2008) and prove parametric lower bounds depending on the size of the alphabet.

This paper is concerned with the many deep and far reaching consequences of Ash’s positive solution of the type II conjecture for finite monoids. After rewieving the statement and history of the problem, we show how it can be used to decide if a finite monoid is in the variety generated by the Malcev product of a given variety and the variety of groups. Many interesting varieties of finite mono...

Most economists, at least when confronted with the issue, would agree that strict selfishness cannot be taken literally as a universal description of the economic agent. For markets to be fully competitive, agents can only be selfish within certain bounds, e.g. they have to respect basic property rights. Also, most employment relationships rely on mutual trust and cooperation. Yet, the selfish,...

We give a polynomial algorithm solving the problem “is S partially confluent on the rational set R?” for finite, basic, noetherian semi-Thue systems. The algorithm is obtained by a polynomial reduction of this problem to the equivalence problem for deterministic 2-tape finite automata, which has been shown to be polynomially decidable in Friedman and Greibach (1982).

A spectral method using fully tensorial rational basis functions on tetrahedron, obtained from the polynomials on the reference cube through a collapsed coordinate transform, is proposed and analyzed. Theoretical and numerical results show that the rational approximation is as accurate as the polynomial approximation, but with a more effective implementation.

We investigate some basic questions about the interaction of regular and rational relations on words. The primary motivation comes from the study of logics for querying graph topology, which have recently found numerous applications. Such logics use conditions on paths expressed by regular languages and relations, but they often need to be extended by rational relations such as subword or subse...

Let ? 2n be the set of paths with 2n steps of unit length in Z 2 , which begin and end at (0; 0). For 2 ? 2n , let area() 2 Z denote the oriented area enclosed by. We show that for every positive even integer k, there exists a rational function R k with integer coeecients, such that: 1 j? 2n j X 2?2n area()] k = R k (n); n > 2k: We calculate explicitly the degree and leading coeecient of R k. W...

In this paper we present algorithms to compute finite state automata which, given any rational language, recognize the languages of normal words and n-chains. We also show how these automata can be used to compute the Hilbert series and Poincaré series for any algebra with a rational set of leading words of its minimal Gröbner basis.

In the classical theory of formal languages, finite state automata allow to recognize the words of a rational subset of Σ∗ where Σ is a set of symbols (or the alphabet). Now, given a semiring (K,+, .), one can construct K-subsets of Σ∗ in the sense of Eilenberg [5], that are alternatively called noncommutative formal power series [2, 13] for which a framework very similar to language theory has...