Abstract We give a short geometric proof of result Soardi and Woess Salvatori that quasitransitive graph is amenable if only its automorphism group unimodular. also strengthen one direction by showing compactly generated totally disconnected locally compact admits proper Lipschitz action on bounded degree then pass via the notion amenability group, which has previously been studied second autho...

Each symmetric matrix A defines a graph homomorphism function ZA(⋅), also known as the partition function. We prove that Bulatov-Grohe dichotomy [4] for ZA(⋅) holds bounded degree graphs. This resolves problem has been open 15 years. Specifically, we any nonnegative with algebraic entries, either ZA(G) is in polynomial time all graphs G, or it #P-hard (and simple) G. further extend complexity t...

Graph homomorphism has been studied intensively. Given an m ×m symmetric matrix A, the graph homomorphism function is defined as

A homomorphism from an oriented graph G to an oriented graph H is an arc-preserving mapping φ from V (G) to V (H), that is φ(x)φ(y) is an arc in H whenever xy is an arc in G. The oriented chromatic number of G is the minimum order of an oriented graph H such that G has a homomorphism to H . The oriented chromatic index of G is the minimum order of an oriented graph H such that the line-digraph ...

Continuing the development [4] of an aspect of the approach to the axiomatization of quantum mechanics of G. W. Mackey [3], we consider here the real linear space X of signed measures on the set P of events generated by the states, and the set F0 of linear functionals on X which are induced in a natural way by the bounded observables. A necessary and sufficient condition for two events to be si...

For a fixed oriented tree T, we consider the complexity of deciding whether or not a given digraph G is homomorphic to T. It was shown by Gutjahr, Woeginger and Welzl that there exist trees T for which this homomorphism problem is NP-complete. However, it seems difficult to decide just which trees T yield NP-complete homomorphism problems. In this paper, we first identify a class of simple tree...

We present a Bounded Model Checking technique for higherorder programs. The vehicle of our study is a higher-order calculus with general references. Our technique is a symbolic state syntactical translation based on SMT solvers, adapted to a setting where the values passed and stored during computation can be functions of arbitrary order. We prove that our algorithm is sound, and devise an opti...

We introduce a notion of an integral along bimonoid homomorphism as simultaneous generalization the and cointegral bimonoids. The purpose this paper is to characterize existence specific integral, called normalized generator in terms kernel cokernel homomorphism. volume on abelian category dimension vector spaces order groups. In applications, we show that there exists nontrivial partially defi...