A partially ordered Abelian group M is algebraically (existentially) closed in a class C M of such structures just in case any finite system of weak inequalities (and negations of weak inequalities), defined over M, is solvable in M if solvable in some N ⊇ M in C. After characterizing existentially closed dimension groups this paper derives amalgamation properties for dimension groups, dimensio...

We prove a direct image theorem stating that the direct image of a Galois formula by a morphism of difference schemes is equivalent to a Galois formula modulo the theory ACFA of existentially closed difference fields. As a consequence, we obtain an effective quantifier elimination procedure and a precise algebraic-geometric description of definable sets over existentially closed difference fiel...

Let T be a strongly minimal theory with quantifier elimination. We show that the class of existentially closed models of T ∪ {“σ is an automorphism”} is an elementary class if and only if T has the definable multiplicity property, as long as T is a finite cover of a strongly minimal theory which does have the definable multiplicity property. We obtain cleaner results working with several automo...

Constraint Handling Rules (CHR) is a concurrent, committed-choice, rule-based language. One of the first CHR programs is the classic constraint solver for syntactic equality of rational trees that performs unification. We first prove its exponential complexity in time and space for non-flat equations and deduce from this proof a quadratic complexity for flat equations. We then present an extend...

We review the characterization of communicating finite-state machines whose behaviors have universally or existentially bounded channels. These results rely on the theory of Mazurkiewicz traces. We investigate the question whether channel bound conditions are decidable for a given communicating finite-state machine.