The weak interactive compression conjecture asserts that any two-party communication protocol with communication complexity C and information complexity I can be compressed to a protocol with communication complexity poly(I)polylog(C). We describe a communication problem that is a candidate for refuting that conjecture. Specifically, while we show that the problem can be solved by a protocol wi...

Planning is an important AI task that gives rise to many hard problems. In order to come up with efficient algorithms for this setting, it is important to understand the sources of complexity. For planning problems that are beyond NP, identifying fragments that allow an efficient reduction to SAT can be a feasible approach due to the great performance of modern SAT solvers. In this paper, we us...

Research on parameterized algorithmics for NP-hard problems has steadily grown over the last years. We survey and discuss how parameterized complexity analysis naturally develops into the field of multivariate algorithmics. Correspondingly, we describe how to perform a systematic investigation and exploitation of the “parameter space” of computationally hard problems. Algorithms and Complexity;...

This paper presents a new intelligent computing approach for combinatorics problems by incorporating logic programming. Permutations, one of the most common and basic topics in combinatorics, appear in many problems in science, engineering, and business. Applications of permutations and other combinatorics problems are briefly reviewed. Implementation of permutations is presented in Prolog, the...

We present some results about the parametric complexity for counting the number of truth assignments for two Conjunctive Forms (2CF’s), such problem is denoted as #2SAT. It is common to analyze the computational complexity for #2SAT regarding the number of variables or the number of clauses on the input formula F We consider here, the time complexity analysis for #2SAT based on a positive integ...