19 research outputs found
CCS with Hennessy's merge has no finite-equational axiomatization
Abstract
This paper confirms a conjecture of Bergstra and Klop¿s from 1984 by establishing that the process algebra obtained by adding an auxiliary operator proposed by Hennessy in 1981 to the recursion free fragment of Milner¿s Calculus of Communicationg Systems is not finitely based modulo bisimulation equivalence. Thus Hennessy¿s merge cannot replace the left merge and communication merge operators proposed by Bergstra and Klop, at least if a finite axiomatization of parallel composition is desired.
2000 MATHEMATICS SUBJECT CLASSIFICATION: 08A70, 03B45, 03C05, 68Q10, 68Q45, 68Q55, 68Q70.
CR SUBJECT CLASSIFICATION (1991): D.3.1, F.1.1, F.1.2, F.3.2, F.3.4, F.4.1.
KEYWORDS AND PHRASES: Concurrency, process algebra, CCS, bisimulation, Hennessy¿s merge, left merge, communication merge, parallel composition, equational logic, complete axiomatizations, non-finitely based algebras
A regular viewpoint on processes and algebra
While different algebraic structures have been proposed for the treatment of concurrency, finding solutions for equations over these structures needs to be worked on further. This article is a survey of process algebra from a very narrow viewpoint, that of finite automata and regular languages. What have automata theorists learnt from process algebra about finite state concurrency? The title is stolen from [31]. There is a recent survey article [7] on finite state processes which deals extensively with rational expressions. The aim of the present article is different. How do standard notions such as Petri nets, Mazurkiewicz trace languages and Zielonka automata fare in the world of process algebra? This article has no original results, and the attempt is to raise questions rather than answer them
A Model of Cooperative Threads
We develop a model of concurrent imperative programming with threads. We
focus on a small imperative language with cooperative threads which execute
without interruption until they terminate or explicitly yield control. We
define and study a trace-based denotational semantics for this language; this
semantics is fully abstract but mathematically elementary. We also give an
equational theory for the computational effects that underlie the language,
including thread spawning. We then analyze threads in terms of the free algebra
monad for this theory.Comment: 39 pages, 5 figure
Free shuffle algebras in language varieties
AbstractWe give simple concrete descriptions of the free algebras in the varieties generated by the “shuffle semirings” LΣ := (P(Σ∗),+,., ⊗, 0,1), or the semirings RΣ := (R(Σ∗),+,., ⊗,∗,0,1), where P(Σ∗) is the collection of all subsets of the free monoid Σ∗, and R(Σ∗) is the collection of all regular subsets. The operation x ⊗ y is the shuffle product
On Kedlaya type inequalities for weighted means
In 2016 we proved that for every symmetric, repetition invariant and Jensen
concave mean the Kedlaya-type inequality holds for an
arbitrary ( stands for the arithmetic mean). We are going
to prove the weighted counterpart of this inequality. More precisely, if
is a vector with corresponding (non-normalized) weights
and denotes the weighted mean then, under
analogous conditions on , the inequality holds for every and such that the sequence
is decreasing.Comment: J. Inequal. Appl. (2018
ON HARDY-TYPE INEQUALITIES FOR WEIGHTED MEANS
Our aim in this article is to establish weighted Hardy-type inequalities in a broad family of means. In other words, for a fixed vector of weights (lambda(n))(n=1)(infinity) and a weighted mean M, we search for the smallest extended real number C such tha