We develop a version of stochastic Pi-calculus with a semantics based on measure theory. We define the behaviour of a process in a rate environment using measures over the measurable space of processes induced by structural congruence. We extend the stochastic bisimulation to include the concept of rate environment and prove that this equivalence is a congruence which extends the structural con...

We prove a congruence criterion for the algebraic theory of power operations in Morava E-theory, analogous to Wilkerson’s congruence criterion for torsion free λ-rings. In addition, we provide a geometric description of this congruence criterion, in terms of sheaves on the moduli problem of deformations of formal groups and Frobenius isogenies.

We call a lattice L isoform, if for any congruence relation Θ of L, all congruence classes of Θ are isomorphic sublattices. We prove that for every finite distributive lattice D, there exists a finite isoform lattice L such that the congruence lattice of L is isomorphic to D.

Contextual equivalence equate terms that have the same observable behaviour in any context. A standard contextual equivalence for CCS is the strong barbed congruence. Configuration structures are a denotational semantics for processes in which one define equivalences that are more discriminating, i.e. that distinguish the denotation of terms equated by barbed congruence. Hereditary history pres...

For an anti-congruence q we say that it is regular anti-congruence on semigroup (S,=, =, ·, α) ordered under anti-order α if there exists an antiorder θ on S/q such that the natural epimorphism is a reverse isotone homomorphism of semigroups. Anti-congruence q is regular if there exists a quasi-antiorder σ on S under α such that q = σ ∪ σ−1. Besides, for regular anti-congruence q on S, a constr...

We introduce a type theoretical framework in which canon ical term rewriting systems can be represented faithfully both from the logical and the computational points of view The framework is based on congruence types a new syntax which combines inductive algebraic and quotient types Congruence types improve on existing work to combine type theories with algebraic rewriting by making explicit th...

OBJECTIVE The ability of alliance to predict outcome has been widely demonstrated, but less is known about the effect of the level of congruence between patient and therapist alliance ratings on outcome. In the current study we examined whether the degree of congruence between patient and therapist alliance ratings can predict symptomatic levels 1 month later in treatment. METHOD The sample c...

We show that noncongruence subgroups of SL2(Z) projectively equivalent to congruence subgroups are ubiquitous. More precisely, they always exist if the congruence subgroup in question is a principal congruence subgroup Γ(N) of level N > 2, and they exist in many cases also for Γ0(N). The motivation for asking this question is related to modular forms: projectively equivalent groups have the sam...

The testing equivalence te that is used as a reference in verification and testing theory in LOTOS is not a congruence, and no explicit definition of the least congruence stronger than te has been found. The critical LOTOS context in which congruence is lost is the hiding context that creates divergence. In this paper we first survey this problem and present three known variants of te that are ...