eprintid: 165
rev_number: 9
eprint_status: archive
userid: 30
dir: disk0/00/00/01/65
datestamp: 2011-03-24 10:41:56
lastmod: 2014-10-07 14:51:25
status_changed: 2011-03-24 10:41:56
type: article
metadata_visibility: show
item_issues_count: 0
creators_name: Lluch-Lafuente, Alberto
creators_name: Montanari, Ugo
creators_id: alberto.lluch@imtlucca.it
creators_id: 
title: Quantitative mu-calculus and CTL Based on Constraint Semirings
ispublished: pub
subjects: QA75
divisions: CSA
full_text_status: public
keywords: Constraint Semirings; Constraints; Temporal Logics; Quantitative Model Checking
note: Proceedings of the Second Workshop on Quantitative Aspects of Programming Languages (QAPL 2004)
abstract: Model checking and temporal logics are boolean. The answer to the model checking question does a system satisfy a property? is either true or false, and properties expressed in temporal logics are defined over boolean propositions. While this classic approach is enough to specify and verify boolean temporal properties, it does not allow to reason about quantitative aspects of systems. Some quantitative extensions of temporal logics has been already proposed, especially in the context of probabilistic systems. They allow to answer questions like with which probability does a system satisfy a property?
We present a generalization of two well-known temporal logics: CTL and the [mu]-calculus. Both extensions are defined over c-semirings, an algebraic structure that captures many problems and that has been proposed as a general framework for soft constraint satisfaction problems (CSP). Basically, a c-semiring consists of a domain, an additive operation and a multiplicative operation, which satisfy some properties. We present the semantics of the extended logics over transition systems, where a formula is interpreted as a mapping from the set of states to the domain of the c-semiring, and show that the usual connection between CTL and [mu]-calculus does not hold in general. In addition, we reason about the feasibility of computing the logics and illustrate some applications of our framework, including boolean model checking.
date: 2005
date_type: published
publication: Electronic Notes in Theoretical Computer Science
volume: 112
publisher: Elsevier
pagerange: 37-59
id_number: 10.1016/j.entcs.2004.02.063
refereed: TRUE
issn: 1571-0661
official_url: http://www.sciencedirect.com/science/article/B75H1-4F7B9RJ-K/2/adc103283079a1187365220a83aad6e5
funders: This work has been supported by the European Research Training Network SEGRAVIS.
citation:   Lluch-Lafuente, Alberto and Montanari, Ugo  Quantitative mu-calculus and CTL Based on Constraint Semirings.  Electronic Notes in Theoretical Computer Science, 112.  pp. 37-59.  ISSN 1571-0661      (2005)  
document_url: http://eprints.imtlucca.it/165/1/Lluch-lafuente-montanari_2004.pdf