Results 1  10
of
52
Automated reasoning in Kleene algebra
 CADE 2007, LNCS 4603
, 2007
"... Abstract. It has often been claimed that model checking, special purpose automated deduction or interactive theorem proving are needed for formal program development. We demonstrate that offtheshelf automated proof and counterexample search is an interesting alternative if combined with the right ..."
Abstract

Cited by 26 (11 self)
 Add to MetaCart
(Show Context)
Abstract. It has often been claimed that model checking, special purpose automated deduction or interactive theorem proving are needed for formal program development. We demonstrate that offtheshelf automated proof and counterexample search is an interesting alternative if combined with the right domain model. We implement variants of Kleene algebras axiomatically in Prover9/Mace4 and perform proof experiments about Hoare, dynamic, temporal logics, concurrency control and termination analysis. They confirm that a simple automated analysis of some important program properties is possible. Particular benefits of this novel approach include “soft ” model checking in a firstorder setting, crosstheory reasoning between standard formalisms and full automation of some (co)inductive arguments. Kleene algebras might therefore provide lightweight formal methods with heavyweight automation. 1
Feature algebra
 IN FORMAL METHODS, VOLUME 4085 OF LNCS
, 2006
"... Based on experience from the hardware industry, product families have entered the software development process as well, since software developers often prefer not to build a single product but rather a family of similar products that share at least one common functionality while having wellidenti ..."
Abstract

Cited by 18 (5 self)
 Add to MetaCart
Based on experience from the hardware industry, product families have entered the software development process as well, since software developers often prefer not to build a single product but rather a family of similar products that share at least one common functionality while having wellidentified variabilities. Such shared commonalities, also called features, reach from common hardware parts to software artefacts such as requirements, architectural properties, components, middleware, or code. We use idempotent semirings as the basis for a feature algebra that allows a formal treatment of the above notions as well as calculations with them. In particular models of feature algebra the elements are sets of products, i.e. product families. We extend the algebra to cover product lines, refinement, product development and product classification. Finally we briefly describe a prototype implementation of one particular model.
Modal Kleene Algebra And Applications  A Survey
, 2004
"... Modal Kleene algebras are Kleene algebras with forward and backward modal operators defined via domain and codomain operations. They provide a concise and convenient algebraic framework that subsumes various other calculi and allows treating quite a variety of areas. We survey ..."
Abstract

Cited by 14 (6 self)
 Add to MetaCart
Modal Kleene algebras are Kleene algebras with forward and backward modal operators defined via domain and codomain operations. They provide a concise and convenient algebraic framework that subsumes various other calculi and allows treating quite a variety of areas. We survey
KATML: An interactive theorem prover for Kleene Algebra with Tests
 University of Manchester
, 2003
"... Abstract. We describe an implementation of an interactive theorem prover for Kleene algebra with tests (KAT). The system is designed to reflect the natural style of reasoning with KAT that one finds in the literature. We illustrate its use with some examples. 1 ..."
Abstract

Cited by 13 (1 self)
 Add to MetaCart
(Show Context)
Abstract. We describe an implementation of an interactive theorem prover for Kleene algebra with tests (KAT). The system is designed to reflect the natural style of reasoning with KAT that one finds in the literature. We illustrate its use with some examples. 1
Termination in Modal Kleene Algebra
 EXPLORING NEW FRONTIERS OF THEORETICAL INFORMATICS. IFIP INTERNATIONAL FEDERATION FOR INFORMATION PROCESSING SERIES 155. KLUWER 2004, 653–666
, 2004
"... Modal Kleene algebras are Kleene algebras with forward and backward modal operators defined via domain and codomain operations. The paper investigates the algebraic structure of modal operators. It studies and compares different notions of termination in this class, including an algebraic correspond ..."
Abstract

Cited by 10 (8 self)
 Add to MetaCart
(Show Context)
Modal Kleene algebras are Kleene algebras with forward and backward modal operators defined via domain and codomain operations. The paper investigates the algebraic structure of modal operators. It studies and compares different notions of termination in this class, including an algebraic correspondence proof of Lob's formula from modal logic. It gives calculational proofs of two fundamental statements from rewriting theory that involve termination: Bachmair's and Dershowitz's wellfounded union theorem and Newman's lemma. These results are also of general interest for the termination analysis of programs and state transition systems.
wp is wlp
 RELATIONAL METHODS IN COMPUTER SCIENCE. LNCS 3929
, 2006
"... Using only a simple transition relation one cannot model commands that may or may not terminate in a given state. In a more general approach commands are relations enriched with termination vectors. We reconstruct this model in modal Kleene algebra. This links the recursive definition of the do od l ..."
Abstract

Cited by 8 (6 self)
 Add to MetaCart
Using only a simple transition relation one cannot model commands that may or may not terminate in a given state. In a more general approach commands are relations enriched with termination vectors. We reconstruct this model in modal Kleene algebra. This links the recursive definition of the do od loop with a combination of the Kleene star and a convergence operator. Moreover, the standard wp operator coincides with the wlp operator in the modal Kleene algebra of commands. Therefore our earlier general soundness and relative completeness proof for Hoare logic in modal Kleene algebra can be reused for wp. Although the definition of the loop semantics is motivated via the standard EgliMilner ordering, the actual construction does not depend on EgliMilnerisotonicity of the constructs involved.
Kleene under a Modal Demonic Star
 JOURNAL ON LOGIC AND ALGEBRAIC PROGRAMMING, SPECIAL ISSUE ON RELATION ALGEBRA AND KLEENE ALGEBRA
, 2004
"... In relational semantics, the inputoutput semantics of a program is a relation on its set of states. We generalize this in considering elements of Kleene algebras as semantical values. In a nondeterministic context, the demonic semantics is calculated by considering the worst behavior of the program ..."
Abstract

Cited by 7 (5 self)
 Add to MetaCart
(Show Context)
In relational semantics, the inputoutput semantics of a program is a relation on its set of states. We generalize this in considering elements of Kleene algebras as semantical values. In a nondeterministic context, the demonic semantics is calculated by considering the worst behavior of the program. In this paper, we concentrate on while loops. Calculating the semantics of a loop is difficult, but showing the correctness of any candidate abstraction is much easier. For deterministic programs, Mills has described a checking method known as the while statement verification rule. A
Modal Kleene Algebra and Partial Correctness
 INSTITUT FÜR INFORMATIK, UNIVERSITÄT AUGSBURG
, 2003
"... We enrich Kleene algebra by domain and codomain operators. These ..."
Abstract

Cited by 7 (7 self)
 Add to MetaCart
We enrich Kleene algebra by domain and codomain operators. These
Calculational RelationAlgebraic Proofs in Isabelle/Isar
 In: Proc. RelMiCS
"... Abstract. We propose a collection of theories in the proof assistant Isabelle/Isar that support calculational reasoning in and about heterogeneous relational algebras and Kleene algebras. 1 Introduction and Related Work Abstract relational algebra is a useful tool for highlevel reasoning that, thr ..."
Abstract

Cited by 7 (0 self)
 Add to MetaCart
(Show Context)
Abstract. We propose a collection of theories in the proof assistant Isabelle/Isar that support calculational reasoning in and about heterogeneous relational algebras and Kleene algebras. 1 Introduction and Related Work Abstract relational algebra is a useful tool for highlevel reasoning that, through appropriate models, provides theorems in fields such as data mining, fuzzy databases, graph transformation, and game theory. Frequently, once an application structure is identified as a model of a particular relationalgebraic theory,