Model counting is of central importance in quantitative reasoning about systems. Examples include computing the probability that a system successfully accomplishes its task without errors, and measuring the number of bits leaked by a system to an adversary in Shannon entropy. Most previous work in those areas demonstrated their analysis on programs with linear constraints, in which cases model ...

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 consider a first-order logic for the integers with addition. This extends classical by modulo-counting, threshold-counting and exact-counting quantifiers, all applied to tuples of variables (here, residues are given as terms while moduli thresholds explicitly). Our main result shows that satisfaction this is decidable in two-fold exponential space. If only threshold- quantifiers allowed, we ...

Due to the physics behind quantum computing, circuit designers must adhere constraints posed by limited interaction distance of qubits. Existing circuits need therefore be modified via insertion SWAP gates, which alter qubit order interchanging location two qubits’ states. We consider Nearest Neighbor Compliance problem on a linear array, where number required gates is minimized. introduce an I...

The class of problems involving the random generation of combinatorial structures from a uniform distribution is considered. Uniform generation problems are, in computational difficulty, intermediate between classical existence and counting problems. It is shown that exactly uniform generation of 'efficiently verifiable' combinatorial structures is reducible to approximate counting (and hence, ...

The parametric lattice-point counting problem is as follows: Given an integer matrix A ∈ Zm×n , compute an explicit formula parameterized by b ∈ R that determines the number of integer points in the polyhedron {x ∈R : Ax É b}. In the last decade, this counting problem has received considerable attention in the literature. Several variants of Barvinok’s algorithm have been shown to solve this pr...