Many compilation problems require computing the control dependence equivalence relation which divides nodes in a control ow graph into equivalence classes such that nodes are in the same class if and only if they have the same set of control dependences. In this paper, we show that this relation can be computed in O(E) time by reducing it to a naturally stated graph problem: in a strongly conne...

Working under large cardinal assumptions, we study the Borel-reducibility between equivalence relations modulo restrictions of the non-stationary ideal on some fixed cardinal κ. We show the consistency of E ++,λ++ λ-club , the relation of equivalence modulo the non-stationary ideal restricted to Sλ ++ λ in the space (λ++)λ ++ , being continuously reducible to E ++ λ+-club , the relation of equi...

‎‎The equivalence relation isoclinism partitions the class of all pairs of groups‎ ‎into families‎. ‎In this paper‎, ‎a complete classification of the set of all pairs $(G,G')$ is established‏‎,‎ whenever‎ $G$ is a $p$-group of order at most $p^5‎‏$‎ and ‎$p$ is a prime number greater than 3. Moreover‎, ‎the classification of pairs $(H,H')$ for extra special $p$-groups $H$ is also given.

1. Overview Notions of program equivalence are fundamental to the process of program speci-cation and transformation. Recent work of Talcott, Mason, and Felleisen establishes a basis for studying notions of program equivalence for programming languages with function and control abstractions operating on objects with memory. This work extends work of Landin, Reynolds, Morris and Plotkin. Landin ...

In this note we introduce a new equivalence relation θ∗ on a (semi)hyperring R and we show that it is strongly regular. Also we prove that, R/θ∗, the equivalence class of this equivalence relation under usual operations consists a commutative (semi-)ring. Finally we introduce the notion of θ-parts of hyperrings and investigate the important properties of them. Mathematics Subject Classification...

In this work we consider modeling of workflow systems with Petri nets. The problem of replacing some resources by others retaining the correct functioning of the system is studied. The relation of resource s-equivalence is defined. Some properties of this relation are studied. It is proved that s-equivalence is decidable provided the set of all minimal sound resources for a given control state ...

We consider the homeomorphism problem for countable topological spaces and investigate its descriptive complexity as an equivalence relation. It is shown that even for countable metric spaces the homeomorphism problem is strictly more complicated than the isomorphism problem for countable graphs and indeed it is not Borel reducible to any orbit equivalence relation induced by a Borel action of ...

In this study, we examine multiple algebras and algebraic structures derived from them and by stating a theory on multiple algebras; we will show that the theory of multiple algebras is a natural extension of the theory of universal algebras. Also, we will treat equivalence relations on multiple algebras, for which the quotient constructed modulo them is a universal algebra and will study the b...

Linearizability and progress properties are key correctness notions for concurrent objects. However, model checking linearizability has suffered from the PSPACE-hardness of the trace inclusion problem. This paper proposes to exploit branching bisimulation, a fundamental semantic equivalence relation developed for process algebras which can be computed efficiently, in checking these properties. ...

In this paper we define an equivalence relation on the set of positive irrational numbers less than 1. The relation is defined by means of continued fractions. Equivalence classes under this relation are determined by the places of some elements equal to 1 (called essential 1’s) in the continued fraction expansion of numbers. Analysis of suprema of all equivalence classes leads to a solution wh...