scholarly journals Concurrent Kleene Algebra with Observations: From Hypotheses to Completeness

2020 ◽  
pp. 381-400
Author(s):  
Tobias Kappé ◽  
Paul Brunet ◽  
Alexandra Silva ◽  
Jana Wagemaker ◽  
Fabio Zanasi
Keyword(s):  
Composition Operator ◽  
Completeness Theorem ◽  
Independent Interest ◽  
Concurrent Programs ◽  
Parallel Composition ◽  
General Study ◽  
Kleene Algebra

AbstractConcurrent Kleene Algebra (CKA) extends basic Kleene algebra with a parallel composition operator, which enables reasoning about concurrent programs. However, CKA fundamentally misses tests, which are needed to model standard programming constructs such as conditionals and $$\mathsf {while}$$ while -loops. It turns out that integrating tests in CKA is subtle, due to their interaction with parallelism. In this paper we provide a solution in the form of Concurrent Kleene Algebra with Observations (CKAO). Our main contribution is a completeness theorem for CKAO. Our result resorts on a more general study of CKA “with hypotheses”, of which CKAO turns out to be an instance: this analysis is of independent interest, as it can be applied to extensions of CKA other than CKAO.

A polynomial-time algorithm for deciding bisimulation equivalence of normed Basic Parallel Processes

1996 ◽  
Vol 6 (3) ◽  
pp. 251-259 ◽  
Author(s):  
Yoram Hirshfeld ◽  
Mark Jerrum ◽  
Faron Moller
Keyword(s):  
Polynomial Time ◽  
Composition Operator ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Parallel Composition ◽  
Elementary Processes ◽  
Parallel Processes ◽  
Bisimulation Equivalence

A polynomial-time algorithm is presented for deciding bisimulation equivalence of so-called Basic Parallel Processes: multisets of elementary processes combined by a commutative parallel-composition operator.

scholarly journals On projecting processes into session types

2012 ◽  
Vol 22 (2) ◽  
pp. 237-289 ◽  
Author(s):  
LUCA PADOVANI
Keyword(s):  
Grounded Theory ◽  
Composition Operator ◽  
Parallel Composition ◽  
Session Types ◽  
Session Type ◽  
Type Preservation

We define session types as projections of the behaviour of processes with respect to the operations processes perform on channels. This calls for a parallel composition operator over session types denoting the simultaneous access to a channel by two or more processes. The proposed approach allows us to define a semantically grounded theory of session types that does not require the linear usage of channels. However, type preservation and progress can only be guaranteed for processes that never receive channels they already own. A number of examples show that the resulting framework validates existing session-type theories and unifies them to some extent.

A FORMULA-DRIVEN MODULAR ATTACK ON STATE EXPLOSION

2002 ◽  
Vol 13 (05) ◽  
pp. 719-731
Author(s):  
Nicoletta De Francesco ◽  
Antonella Santone
Keyword(s):  
Distributed Systems ◽  
Model Checking ◽  
State Space ◽  
Composition Operator ◽  
The State ◽  
Parallel Composition ◽  
State Explosion ◽  
State Explosion Problem ◽  
Parallel Processes ◽  
Compositional Method

A common characteristic of the new distributed systems is the increasing complexity. Useful paradigms to cope with the complexity of systems are modularity and compositionality. In this paper we define a compositional method to attack the state explosion problem in model checking. The method, given a formula to be checked on a system composed of a set of parallel processes, allows syntactically reducing in a modular way the processes, in order to reduce the state space of their composition. The reduction is formula driven and is based on a notion of equivalence between processes, which is a congruence w.r.t. the parallel composition operator.

FORWARD ANALYSIS OF DYNAMIC NETWORK OF PUSHDOWN SYSTEMS IS EASIER WITHOUT ORDER

2011 ◽  
Vol 22 (04) ◽  
pp. 843-862 ◽  
Author(s):  
DENIS LUGIEZ
Keyword(s):  
Static Analysis ◽  
Dynamic Networks ◽  
Dynamic Network ◽  
Concurrent Programs ◽  
Parallel Composition ◽  
Tree Automata ◽  
Weighted Tree ◽  
Weighted Automata ◽  
Forward Analysis ◽  
Weighted Tree Automata

Dynamic networks of Pushdown Systems (DNPS in short) have been introduced to perform static analysis of concurrent programs that may spawn threads dynamically. In this model the set of successors of a regular set of configurations can be non-regular, making forward analysis of these models difficult. We refine the model by adding the associative-commutative properties of parallel composition, and we define Presburger weighted tree automata, an extension of weighted automata and tree automata, that accept the set of successors of a regular set of configurations. This yields decidability of the forward analysis of DNPS. Finally, we extend this result to the model where configurations are sets of threads running in parallel.

scholarly journals Models of Concurrent Kleene Algebra

10.29007/qp92 ◽  
2020 ◽  
Author(s):  
Alexandra Silva
Keyword(s):  
Concurrent Programs ◽  
Sequential Consistency ◽  
Partial Observations ◽  
Control Structures ◽  
Kleene Algebra ◽  
Ongoing Work ◽  
Algebraic Framework ◽  
Memory Accesses ◽  
The Right ◽  
Partially Observable

Kleene Algebra and variants thereof have been successfully used in verification of se- quential programs. The leap to concurrent programs offers many challenges, both in terms of devising the right foundations to study concurrent variants of Kleene Algebra but also in finding the right models to enable effective verification of relevant programs. In this talk, we will review existing and ongoing work on concurrent Kleene Algebra with a focus on a variant called partially observable concurrent Kleene algebra (POCKA). POCKA offers an algebraic framework to reason about concurrent programs with control structures, such as conditionals and loops. We will show how a previously developed technique for com- pleteness of Kleene Algebra can be lifted to prove that POCKA is a sound and complete axiomatization of a model of partial observations. We illustrate the use of the framework in the analysis of sequential consistency, i.e., whether programs behave as if memory accesses taking place were interleaved and executed sequentially.The work described in this invited talk is based on [1, 2, 3], and it is joint with a won- derful group of people: Paul Brunet, Simon Docherty, Tobias Kapp ́e, Jurriaan Rot, Jana Wagemaker, and Fabio Zanasi.

A system of functions biorthogonal with the derivatives of Chebyshev second-kind polynomials of a complex variable

2020 ◽  
Vol 17 (2) ◽  
pp. 256-277
Author(s):  
Ol'ga Veselovska ◽  
Veronika Dostoina
Keyword(s):  
Complex Plane ◽  
Complex Variable ◽  
Analytic Functions ◽  
Combinatorial Identities ◽  
Independent Interest ◽  
Closed Curves ◽  
In Series ◽  
Derivatives Of

For the derivatives of Chebyshev second-kind polynomials of a complex vafiable, a system of functions biorthogonal with them on closed curves of the complex plane is constructed. Properties of these functions and the conditions of expansion of analytic functions in series in polynomials under consideration are established. The examples of such expansions are given. In addition, we obtain some combinatorial identities of independent interest.

On Statman's Finite Completeness Theorem

1992 ◽  
Author(s):  
Richard Statman ◽  
Gilles Dowek
Keyword(s):  
Completeness Theorem

Flat functors and classifying toposes

2018 ◽  
Author(s):  
Olivia Caramello
Keyword(s):  
General Theory ◽  
Geometric Theory ◽  
Small Category ◽  
Independent Interest ◽  
Yoneda Lemma ◽  
Geometric Morphisms ◽  
The Way

This chapter develops a general theory of extensions of flat functors along geometric morphisms of toposes; the attention is focused in particular on geometric morphisms between presheaf toposes induced by embeddings of categories and on geometric morphisms to the classifying topos of a geometric theory induced by a small category of set-based models of the latter. A number of general results of independent interest are established on the way, including developments on colimits of internal diagrams in toposes and a way of representing flat functors by using a suitable internalized version of the Yoneda lemma. These general results will be instrumental for establishing in Chapter 6 the main theorem characterizing the class of geometric theories classified by a presheaf topos and for applying it.

Sign in / Sign up

Export Citation Format

Share Document