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Integration of Sequential Scenarios
 IEEE Transactions on Software Engineering
, 1998
"... Abstract—We give a formal relationbased definition of scenarios and we show how different scenarios can be integrated to obtain a more global view of usersystem interactions. We restrict ourselves to the sequential case, meaning that we suppose that there is only one user (thus, the scenarios we w ..."
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Cited by 18 (2 self)
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Abstract—We give a formal relationbased definition of scenarios and we show how different scenarios can be integrated to obtain a more global view of usersystem interactions. We restrict ourselves to the sequential case, meaning that we suppose that there is only one user (thus, the scenarios we wish to integrate cannot occur concurrently). Our view of scenarios is statebased, rather than eventbased, like most of the other approaches, and can be grafted to the wellestablished specification language Z. Also, the end product of scenario integration, the specification of the functional aspects of the system, is given as a relation; this specification can be refined using independently developed methods. Our formal description is coupled with a diagrambased, transitionsystem like, presentation of scenarios, which is better suited to communication between clients and specifiers. Index Terms—Scenario, integration, usersystem interaction, requirements elicitation, relational approach, statebased approach. 1
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 ..."
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Cited by 8 (6 self)
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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 ..."
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Cited by 7 (5 self)
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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
Algebraic Separation Logic
, 2010
"... We present an algebraic approach to separation logic. In particular, we give an algebraic characterisation for assertions of separation logic, discuss different classes of assertions and prove abstract laws fully algebraically. After that, we use our algebraic framework to give a relational semantic ..."
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Cited by 5 (4 self)
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We present an algebraic approach to separation logic. In particular, we give an algebraic characterisation for assertions of separation logic, discuss different classes of assertions and prove abstract laws fully algebraically. After that, we use our algebraic framework to give a relational semantics of the commands of the simple programming language associated with separation logic. On this basis we prove the frame rule in an abstract and concise way. We also propose a more general version of separating conjunction which leads to a frame rule that is easier to prove. In particular, we show how to algebraically formulate the requirement that a command does not change certain variables; this is also expressed more conveniently using the generalised separating conjunction. The algebraic view does not only yield new insights on separation logic but also shortens proofs due to a point free representation. It is largely firstorder and hence enables the use of offtheshelf automated theorem provers for verifying properties at a more abstract level.
The Demonic Product of Probabilistic Relations
, 2001
"... The demonic product of two probabilistic relations is defined and investigated. It is shown that the product is stable under bisimulations when the mediating object is probabilistic, and that under some mild conditions the nondeterministic fringe of the probabilistic relations behaves properly: the ..."
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Cited by 3 (1 self)
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The demonic product of two probabilistic relations is defined and investigated. It is shown that the product is stable under bisimulations when the mediating object is probabilistic, and that under some mild conditions the nondeterministic fringe of the probabilistic relations behaves properly: the fringe of the product equals the demonic product of the fringes.
Modal design algebra
 PROC. FIRST INTERNATIONAL SYMPOSIUM ON UNIFYING THEORIES OF PROGRAMMING. LNCS
"... We give an algebraic model of (H3) designs based on a variant of modal semirings, hence generalising the original relational model. This makes the theory applicable to a wider class of settings, e.g., to algebras of sets of traces. Moreover, we set up the connection with the weakly and strongly demo ..."
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Cited by 2 (1 self)
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We give an algebraic model of (H3) designs based on a variant of modal semirings, hence generalising the original relational model. This makes the theory applicable to a wider class of settings, e.g., to algebras of sets of traces. Moreover, we set up the connection with the weakly and strongly demonic semantics of programs as discussed by a number of authors. This is done using commands (a, t) where a corresponds to the transition relation of a program and the condition t characterises the input states from which termination is guaranteed. The commands form not only a semiring but even a Kleene and omega algebra. This is used to calculate closed expressions for the least and greatest fixed point semantics of the demonic while loop.
Network Algebra with Demonic Relation Operators
"... Relations with demonic operators are used in studies related to predicate transformer semantics of nondeterministic programs, to model the connection wires in synchronous dataflow networks, or in process algebra setting to model the communication between agents and their envirnoments. The aim of thi ..."
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Relations with demonic operators are used in studies related to predicate transformer semantics of nondeterministic programs, to model the connection wires in synchronous dataflow networks, or in process algebra setting to model the communication between agents and their envirnoments. The aim of this paper is to provide equational axiomatisations for various classes of finite relations with demonic (including looping) operators. We present axiomatisations for three types of demonic calculi: i.e. calculi for relations with forward demonic , backward demonic  or twoway demonic operators. The algebraic structures involved are basic network algebras (a certain class of symmetric strict monoidal categories enriched with a looping operation  feedback) with appropriate ramification and identification constants. Keywords & Phrases: network algebra, relations, demonic calculus, synchronous dataflow networks, feedback. The second author has been partially supported by the HCM Cooperati...
From System Requirements to Software Requirements in the FourVariable Model
"... Abstract: The fourvariable model of softwarecontrolled embedded systems [PM95] has been used successfully in safetycritical applications. The model does not explicitly specify the software requirements, but rather bounds them by specifying the system requirements and the input and output hardware ..."
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Abstract: The fourvariable model of softwarecontrolled embedded systems [PM95] has been used successfully in safetycritical applications. The model does not explicitly specify the software requirements, but rather bounds them by specifying the system requirements and the input and output hardware interfaces of the system. The software engineers are left with the problem of how to construct software that satisfies the system requirements and hardware interfacing constraints. After formalizing the properties of acceptable system and software implementations using the demonic calculus of relations, we provide (i) necessary and sufficient conditions for the existence of an acceptable software implementation and (ii) a mathematical characterization of the software requirements in terms of their weakest specification.
The Journal of Logic and Algebraic Programming
"... This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal noncommercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or sel ..."
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This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal noncommercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier’s archiving and manuscript policies are encouraged to visit: