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On the Structure of Inductive Reasoning: Circular and TreeShaped Proofs in the µCalculus
 IN PROCEEDINGS OF FOSSACS 2003
, 2003
"... In this paper we study induction in the context of the firstorder µcalculus with explicit approximations. We present and compare two Gentzenstyle proof systems each using a different type of induction. The first is ..."
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Cited by 20 (2 self)
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In this paper we study induction in the context of the firstorder µcalculus with explicit approximations. We present and compare two Gentzenstyle proof systems each using a different type of induction. The first is
Compositional Verification of Secure Applet Interactions
 Fundamental Approaches to Software Engineering (FASE'02), number 2306 in LNCS
, 2002
"... Recent developments in mobile code and embedded systems have lead to an increased interest in open platforms, i.e. platforms which enable different applications to interact in a dynamic environment. However, the flexibility of open platforms presents major difficulties for the (formal) verification ..."
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Cited by 12 (3 self)
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Recent developments in mobile code and embedded systems have lead to an increased interest in open platforms, i.e. platforms which enable different applications to interact in a dynamic environment. However, the flexibility of open platforms presents major difficulties for the (formal) verification of secure interaction between the different applications. To overcome these difficulties, compositional verification techniques are required. This paper presents a compositional approach to the specification and verification of secure applet interactions. This approach involves a compositional model of the interface behavior of applet interactions, a temporal logic property specification language, and a proof system for proving correctness of property decompositions. The usability of the approach is demonstrated on a realistic smartcard case study.
Sequent Calculi for Process Verification: HennessyMilner Logic for an Arbitrary GSOS
, 2003
"... We argue that, by supporting a mixture of “compositional” and “structural” styles of proof, sequentbased proof systems provide a useful framework for the formal verification of processes. As a worked example, we present a sequent calculus for establishing that processes from a process algebra satis ..."
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Cited by 11 (1 self)
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We argue that, by supporting a mixture of “compositional” and “structural” styles of proof, sequentbased proof systems provide a useful framework for the formal verification of processes. As a worked example, we present a sequent calculus for establishing that processes from a process algebra satisfy assertions in HennessyMilner logic. The main novelty lies in the use of the operational semantics to derive introduction rules, on the left and right of sequents, for the operators of the process calculus. This gives a generic proof system applicable to any process algebra with an operational semantics specified in the GSOS format. Using a general algebraic notion of GSOS model, we prove a completeness theorem for the cutfree fragment of the proof system, thereby establishing the admissibility of the cut rule. Under mild (and necessary) conditions on the process algebra, an ωcompleteness result, relative to the “intended” model of closed process terms, follows.
A Note on Global Induction Mechanisms in a µCalculus with Explicit Approximations
, 1999
"... We investigate a Gentzenstyle proof system for the firstorder µcalculus based on cyclic proofs, produced by unfolding fixed point formulas and detecting repeated proof goals. Our system uses explicit ordinal variables and approximations to support a simple semantic induction discharge conditio ..."
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Cited by 9 (0 self)
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We investigate a Gentzenstyle proof system for the firstorder µcalculus based on cyclic proofs, produced by unfolding fixed point formulas and detecting repeated proof goals. Our system uses explicit ordinal variables and approximations to support a simple semantic induction discharge condition which ensures the wellfoundedness of inductive reasoning. As the main result of this paper we propose a new syntactic discharge condition based on traces and establish its equivalence with the semantical condition. We give an automatatheoretic reformulation of this condition which is more suitable for practical proofs. For a detailed
Compositional Verification of CCS Processes
, 1999
"... . We present a proof system for verifying CCS processes in the modal ¯calculus. Its novelty lies in the generality of the proof judgements allowing parametric and compositional reasoning in this complex setting. This is achieved, in part, by the use of explicit fixed point ordinal approximations, a ..."
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Cited by 8 (4 self)
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. We present a proof system for verifying CCS processes in the modal ¯calculus. Its novelty lies in the generality of the proof judgements allowing parametric and compositional reasoning in this complex setting. This is achieved, in part, by the use of explicit fixed point ordinal approximations, and in part by a complete separation, following an approach by Simpson, of rules concerning the logic from the rules encoding the operational semantics of the process language. 1 Introduction In a number of recent papers [14, 9] prooftheoretical frameworks for compositional verification have been put forward based on Gentzenstyle sequents of the shape \Gamma ` \Delta, where the components of \Gamma and \Delta are correctness assertions P : OE. Several programming or modelling languages have been considered, including CCS [3], the ßcalculus [2], CHOCS [1], general GSOSdefinable languages [9], and even a significant core fragment of a real programming language, Erlang [4]. An important ...
Verifying Temporal Properties Using Explicit Approximants: Completeness for Contextfree Processes
 In FOSSACS '02
, 2002
"... We present a sequent calculus for formally verifying modal calculus properties of concurrent processes. Building on work by Dam and Gurov, the proof system contains rules for the explicit manipulation of fixedpoint approximants. We develop a new syntax for approximants, incorporating, in particula ..."
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We present a sequent calculus for formally verifying modal calculus properties of concurrent processes. Building on work by Dam and Gurov, the proof system contains rules for the explicit manipulation of fixedpoint approximants. We develop a new syntax for approximants, incorporating, in particular, a mechanism for approximant modification. We make essential use of this feature to prove our main result: the sequent calculus is complete for establishing arbitrary calculus properties of contextfree processes.
Canonical completeness of infinitary µ
 Submitted. Address Thomas Studer Institut für Informatik und angewandte Mathematik, Universität Bern Neubrückstrasse 10, CH3012
"... This paper presents a new model construction for a natural cutfree infinitary version K + ω (µ) of the propositional modal µcalculus. Based on that the completeness of K + ω (µ) and the related system Kω(µ) can be established directly – no detour, for example through automata theory, is needed. As ..."
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This paper presents a new model construction for a natural cutfree infinitary version K + ω (µ) of the propositional modal µcalculus. Based on that the completeness of K + ω (µ) and the related system Kω(µ) can be established directly – no detour, for example through automata theory, is needed. As a side result we also obtain a finite, cutfree sound and complete system for the propositional modal µcalculus. 1
A Tool for Verifying Software Written in Erlang
, 2000
"... The present paper presents an overview of the main results of the ASTEC project Verication of Erlang Programs, focusing in particular on the Erlang verication tool. This is a theoremproving tool which assists in obtaining proofs that Erlang applications satisfy their correctness requirements f ..."
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The present paper presents an overview of the main results of the ASTEC project Verication of Erlang Programs, focusing in particular on the Erlang verication tool. This is a theoremproving tool which assists in obtaining proofs that Erlang applications satisfy their correctness requirements formulated in a specication logic. We give a summary of the verication framework as supported by the tool, discuss reasoning principles essential for successful verication such as inductive and compositional reasoning, and an ecient treatment of sideeectfree code. The experiences of applying the verication tool in an industrial case study are summarised, and an approach for supporting verication in the presence of program libraries is outlined. The verication tool is essentially a classical proof assistant, or theoremproving tool, requiring users to intervene in the proof process at crucial steps such as stating program invariants. However, the tool oers considerable su...
Compositional Specification and Verification of Control Flow Based Security Properties of MultiApplication Programs
, 2001
"... Jensen et al. present a simple and elegant program model, within a specification and verification framework for checking control flow based security properties by model checking techniques. We generalise this model and framework to allow for compositional specification and verification of security p ..."
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Jensen et al. present a simple and elegant program model, within a specification and verification framework for checking control flow based security properties by model checking techniques. We generalise this model and framework to allow for compositional specification and verification of security properties of multiapplication programs. The framework contains a program model for multiapplication programs, and a temporal logic to specify security properties about such programs.