Related papers: Complexity of Atoms, Combinatorially
We introduce and study logic programs whose clauses are built out of monotone constraint atoms. We show that the operational concept of the one-step provability operator generalizes to programs with monotone constraint atoms, but the…
We present a new approach to formal language theory using Kolmogorov complexity. The main results presented here are an alternative for pumping lemma(s), a new characterization for regular languages, and a new method to separate…
Received wisdom in linguistic typology holds that if the structure of a language becomes more complex in one dimension, it will simplify in another, building on the assumption that all languages are equally complex (Joseph and Newmeyer,…
Multitildes are regular operators that were introduced by Caron et al. in order to increase the number of Glushkov automata. In this paper, we study the family of the multitilde operators from an algebraic point of view using the notion of…
Let $M$ be a cancellative and commutative monoid (written additively). The monoid $M$ is atomic if every non-invertible element can be written as a sum of irreducible elements (often called atoms in the literature). Weaker versions of…
The avoidability, or unavoidability of patterns in words over finite alphabets has been studied extensively. A word (pattern) over a finite set is said to be unavoidable if, for all but finitely many words, there exists a morphism mapping…
We study regular expressions that use variables, or parameters, which are interpreted as alphabet letters. We consider two classes of languages denoted by such expressions: under the possibility semantics, a word belongs to the language if…
We introduce a flexible class of well-quasi-orderings (WQOs) on words that generalizes the ordering of (not necessarily contiguous) subwords. Each such WQO induces a class of piecewise testable languages (PTLs) as Boolean combinations of…
A regular language $L$ is said to be prime, if it is not the product of two non-trivial languages. Martens et al. settled the exact complexity of deciding primality for deterministic finite automata in 2010. For finite languages, Mateescu…
Real atomic systems, like the hydrogen atom in a magnetic field or the helium atom, whose classical dynamics are chaotic, generally present both discrete and continuous symmetries. In this letter, we explain how these properties must be…
The quasicontinuum (QC) method, originally proposed by Tadmor, Ortiz and Phillips in 1996, is a computational technique that can efficiently handle regular atomistic lattices by combining continuum and atomistic approaches. In the present…
The height of a piecewise-testable language $L$ is the maximum length of the words needed to define $L$ by excluding and requiring given subwords. The height of $L$ is an important descriptive complexity measure that has not yet been…
Team Semantics generalizes Tarski's Semantics for First Order Logic by allowing formulas to be satisfied or not satisfied by sets of assignments rather than by single assignments. Because of this, in Team Semantics it is possible to extend…
We compute the exact maximum state complexity for the language consisting of $m$ words of length $N$, and characterize languages achieving the maximum. We also consider a special case, namely languages $C(w)$ consisting of the conjugates of…
In [Math. Proc. Cambridge Philos. Soc. 64 (1968), 251-264], P.M. Cohn famously claimed that a commutative domain is atomic if and only if it satisfies the ascending chain condition on principal ideals (ACCP). Some years later, a…
Recent optical-potential studies of the phenomenology of kaonic atoms are reviewed. It is shown that the data can be fitted by a complex optical potential with either a relatively shallow attractive component (about -50 MeV at…
We consider the problem of enumerating a regular language $L$ in radix order, or more precisely, the equivalent problem of enumerating all words in $L$ of a given length in lexicographic order. Ackerman and Shallit gave in 2009 the…
Let $S$ be a finite alphabet. An injective word over $S$ is a word over $S$ such that each letter in $S$ appears at most once in the word. We study Boolean cell complexes of injective words over $S$ and their commutation classes. This…
It is shown that $\alpha^2$-term of sum rules for the total cross sections of interaction of elementary atoms with matter ones, obtained in ref.[Denisenko K. and Mrowczynski S., Phys. Rev. D36 (1987) 1529] is wrong. New sum rules valid up…
This paper presents a new solution to the containment problem for extended regular expressions that extends basic regular expressions with intersection and complement operators and consider regular expressions on infinite alphabets based on…