We give an FPRAS for Holant problems with parity constraints and not-all-equal constraints, a generalisation of the problem of counting sink-free-orientations. The approach combines a sampler for near-assignments of “windable” functions – using the cycle-unwinding canonical paths technique of Jerrum and Sinclair – with a bound on the weight of nearassignments. The proof generalises to a larger ...

We give characterizations of nondeterministic complexity classes such as NP and PSPACE and the classes in the polynomial time hierarchy in the two-person pebble game model [VT89]. These characterizations motivate the definitions of these classes using firstorder sentences extending the results in [Im82]. It is shown that the role-switches resource in the pebble games closely model the levels of...

Compton, K.J., Stratified least fixpoint logic, Theoretical Computer Science 131 (1994) 95-120. Stratified least jixpoint logic, or SLFP, characterizes the expressibility of stratified logic programs and, in a different formulation, has been used as a logic of imperative programs. These two formulations of SLFP are proved to be equivalent. A complete sequent calculus with one infinitary rule is...

We investigate in an algebraic setting the question in which logical languages the properties integral, permutational, and rigid of algebras of relations can be expressed.

We consider several open problems of Karhum aki, Mignosi, and Plandowski, cf. [KMP], concerning the expressibility of languages and relations as solutions of word equations. We show rst that the (scattered) subword relation is not expressible. Then, we consider the set of k-power free nite words and solve it negativelly for all nontrivial integer values of k. Finally, we consider the Fibonacci...

The hybrid quantum-classical algorithm is actively examined as a technique applicable even to intermediate-scale quantum computers. To execute this algorithm, the hardware efficient ansatz often used, thanks its implementability and expressibility; however, has critical issue in trainability sense that it generically suffers from so-called gradient vanishing problem. This can be resolved by lim...