Probabilistic inference via model counting has emerged as a scalable technique with strong formal guarantees, thanks to recent advances in hashing-based approximate counting. State-of-theart hashing-based counting algorithms use an NP oracle (SAT solver in practice), such that the number of oracle invocations grows linearly in the number of variables n in the input constraint. We present a new ...

Following the approach of Hemaspaandra and Vollmer, we can define counting complexity classes #·C for any complexity class C of decision problems. In particular, the classes #·ΠkP with k ≥ 1 corresponding to all levels of the polynomial hierarchy have thus been studied. However, for a large variety of counting problems arising from optimization problems, a precise complexity classification turn...

We give characterizations of strong determinism for regular expressions with counting, based on which we present an O(|ΣE ||E|) time algorithm to check whether an expression E with counting is strongly deterministic where ΣE is the set of distinct symbols in E. It improves the previous upper bound of O(|E|) time on the same decision problems for both standard regular expressions and regular exp...

We investigate the computational complexity of the problem of counting the locally maximal satisfying assignments of a Constraint Satisfaction Problem (CSP) over the Boolean domain {0, 1}. A satisfying assignment is locally maximal if any new assignment which is obtained from it by changing a 0 to a 1 is unsatisfying. For each constraint language Γ, #LocalMaxCSP(Γ) denotes the problem of counti...

We investigate the model counting problem for safety specifications expressed in linear-time temporal logic (LTL). Model counting has previously been studied for propositional logic; in planning, for example, propositional model counting is used to compute the plan’s robustness in an incomplete domain. Counting the models of an LTL formula opens up new applications in verification and synthesis...

The Omega polynomial(x) was recently proposed by Diudea, based on the length of strips in given graph G. The Sadhana polynomial has been defined to evaluate the Sadhana index of a molecular graph. The PI polynomial is another molecular descriptor. In this paper we compute these three polynomials for some infinite classes of nanostructures.

A new approach is proposed to the calibration of photodetectors and the determination of the absolute value of the quantum efficiency of photon-counting photomultipliers using entangled-photon pairs. It is based on a new single-photodetector technique and a special modulation of the entangled-photon flux. The absolute values of the quantum efficiency have been determined for several photon-coun...

We present new functional equations connecting the counting series of plane and planar (in the sense of Harary and Palmer) dissections. Simple rigorous expressions for counting symmetric r-dissections of polygons and planar S-dissections are obtained.