We investigate the structure of “worst-case” quasi reduced ordered decision diagrams and Boolean functions whose truth tables are associated to: we suggest different ways to count and enumerate them. We, then, introduce a notion of complexity which leads to the concept of “hard” Boolean functions as functions whose QROBDD are “worst-case” ones. So we exhibit the relation between hard functions and the Storage Access function (also known as Multiplexer).
We investigate the structure of “worst-case” quasi reduced ordered decision diagrams and Boolean functions whose truth tables are associated to: we suggest different ways to count and enumerate them. We, then, introduce a notion of complexity which leads to the concept of “hard” Boolean functions as functions whose QROBDD are “worst-case” ones. So we exhibit the relation between hard functions and the Storage Access function (also known as Multiplexer).
We show that some classical P-complete problems can be solved efficiently in average NC. The probabilistic model we consider is the sample space of input descriptions of the problem with the underlying distribution being the uniform one. We present parallel algorithms that use a polynomial number of processors and have expected time upper bounded by (e ln 4 + o(1))log n, asymptotically with high probability, where n is the instance size.
Ordered binary decision diagrams (OBDDs) and several more general BDD models have turned out to be representations of Boolean functions which are useful in applications like verification, timing analysis, test pattern generation or combinatorial optimization. The hidden weighted bit function (HWB) is of particular interest, since it seems to be the simplest function with exponential OBDD size. The complexity of this function with respect to different circuit models, formulas, and various...
We prove that for any additive hereditary property P > O, it is NP-hard to decide if a given graph G allows a vertex partition V(G) = A∪B such that G[A] ∈ 𝓞 (i.e., A is independent) and G[B] ∈ P.
We investigate the complexity of languages described by some expressions containing shuffle operator and intersection. We show that deciding whether the shuffle of two words has a nonempty intersection with a regular set (or fulfills some regular pattern) is NL-complete. Furthermore we show that the class of languages of the form , with a shuffle language and a regular language , contains non-semilinear languages and does not form a family of mildly context- sensitive languages.
We investigate the complexity of languages described by some expressions containing shuffle operator and intersection. We show that deciding whether the shuffle of two words has a nonempty intersection with a regular set (or fulfills some regular pattern) is NL-complete. Furthermore we show that the class of languages of the form , with a shuffle language L and a regular language R, contains non-semilinear languages and does not form a family of mildly context- sensitive languages.
A real number x is called Δ20 if its binary expansion corresponds to a Δ20-set of natural numbers. Such reals are just the limits of computable sequences of rational numbers and hence also called computably approximable. Depending on how fast the sequences converge, Δ20-reals have different levels of effectiveness. This leads to various hierarchies of Δ20 reals. In this survey paper we summarize several recent developments related to such kind of hierarchies shown by the author and his collaborators. ...
In this paper we study the parameterized complexity of approximating the parameterized counting problems contained in the class , the parameterized analogue of . We prove a parameterized analogue of a famous theorem of Stockmeyer claiming that approximate counting belongs to the second level of the polynomial hierarchy.
In this paper we study the parameterized complexity of approximating the parameterized counting problems contained in the class , the parameterized analogue of . We prove a parameterized analogue of a famous theorem of Stockmeyer claiming that approximate counting belongs to the second level of the polynomial hierarchy.
We display a complexity notion based on the syntax of a tree series which yields two distinct hierarchies, one within the class of recognizable tree series and another one in the class of non-recognizable tree series.
We consider the question of which loops are capable of expressing arbitrary Boolean functions through expressions of constants and variables. We call this property Boolean completeness. It is a generalization of functional completeness, and is intimately connected to the computational complexity of various questions about expressions, circuits, and equations defined over the loop. We say that a loop is polyabelian if it is an iterated affine quasidirect product of Abelian groups; polyabelianness...