J. Rathke. Symbolic Techniques for Value-passing Calculi. Ph.D Thesis, University of Sussex, 1997.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....which the passing of time can be observed, and value passing systems, in which the system may be observed to input and output values along named ports. The values may even be names themselves, as in the pi calculus. A large number of extensions of popular logics has been proposed (for example, in [2, 1, 4]) but there is as yet no common framework in which the extensions can be studied. This seems unfortunate, since in fact the extensions have a great deal in common. In this paper we consider the problem of de ning an assembly language logic for such extensions. The logic should be small and ....

.... [ d d] p q) Finally, the T x point, which is formally parametrized on clock environments, is translated directly to an A x point, formally parametrized on cell environments. 3. 3 Value passing mu calculus As sketched earlier, we can also handle value passing logics such as [1, 4]. As an example we translate Dam s rst order mu calculus for the pi calculus, which we will call P . The main diculty, which is presentational rather than substantial, stems from Dam s explicit use of abstractions and concretions, both in the pi calculus and in the logic. An abstraction is an ....

J. Rathke, Symbolic Techniques for Value-Passing Calculi. PhD. thesis, University of Sussex, 1997.

....processes. We only give an overview of the model and we refer to [8] for a complete discussion. An SGA (Symbolic Graph with Assignment) is a rooted directed graph where each node n has an associated finite set of free variables fv(n) and each edge is labeled by a guarded action with assignment [11, 17]. Note that a node in SGA is an ACSR VP term. The notion of a substitution, which we also call assignment, is defined as follows. A substitution is any function : X Expr, such that (x) 6= x for a finite number of x 2 X. Given a substitution , the support (or domain) of is the set of ....

J. Rathke. Symbolic Techniques for Value-passing Calculi. PhD thesis, University of Sussex, 1997.

....Rather than basis the reasoning for concluding that a least fixed point holds on an inductive argument on the set of states under which it is unfolded, Gurov [Gur98] motivates discharge based on an inductive argument external to the proof system about the domain of values considered. Rathke [Rat97] also considers a local proof system using the tagging approach for model checking value passing processes but here the underlying models for value passing processes are symbolic graphs. Dam [Dam98] considers the verification of infinite state systems described in CCS using a compositional proof ....

J. Rathke. Symbolic Techniques for Value-Passing Calculi. PhD thesis, University of Sussex, 1997.

....which the passing of time can be observed, and value passing systems, in which the system may be observed to input and output values along named ports. The values may even be names themselves, as in the pi calculus. A large number of extensions of popular logics has been proposed (for example, in [2, 1, 4]) but there is as yet no common framework in which the extensions can be studied. This seems unfortunate, since in fact the extensions have a great deal in common. In this paper we consider the problem of de ning an assembly language logic for such extensions. The logic should be small and ....

....fd 0 g; d 0 d] p q) Finally, the T x point, which is formally parametrized on clock environments, is translated directly to an A x point, formally parametrized on cell environments. 3. 3 Value passing mu calculus As sketched earlier, we can also handle value passing logics such as [1, 4]. As an example we translate Dam s rst order mu calculus for the pi calculus, which we will call P . The main diculty, which is presentational rather than substantial, stems from Dam s explicit use of abstractions and concretions, both in the pi calculus and in the logic. An abstraction is an ....

J. Rathke, Symbolic Techniques for Value-Passing Calculi. PhD. thesis, University of Sussex, 1997.

....of and oe is the substitution denoted by ; oe such that for every variable x, oe(x) oe( x) We often write oe for ; oe. An SGA is a rooted directed graph where each node n has an associated finite set of free variables fv(n) and each edge is labeled by a guarded action with assignment [16, 23]. Note that a node in SGA is a ACSR VP term. Definition 2.1 (SGA) A Symbolic Graph with Assignment (SGA) for ACSR VP is a rooted directed graph where each node n has an associated ACSR VP term and each edge is labeled by boolean, action, assignment, b; ff; 1) Gamma ff:P true;ff;Id ....

Julian Rathke. Symbolic Techniques for Value-passing Calculi. PhD thesis, University of Sussex, 1997.

....done externally to the present proof system. Proof systems of the above kind have been the focus of many research papers and dissertations. These papers differ from our approach in that they refer to the LTS of the system being verified instead of the process description itself (as for example in [Cle90, SW91, Bra92, BS92, And93, Dam93, HL95, Rat97, RH97]) or in that they consider propositional modal calculus formulae only, i.e. do not address value passing (as in most of the above references, as well as in [ASW94, Dam95] Value Passing Our interest in value passing comes from the fact that many communicating systems do not just carry around ....

Julian Rathke. Symbolic Techniques for Value-passing Calculi. PhD thesis, School of Cognitive and Computing Sciences, University of Sussex, United Kingdom, March 1997.

....which the passing of time can be observed, and value passing systems, in which the system may be observed to input and output values along named ports. The values may even be names themselves, as in the pi calculus. A large number of extensions of popular logics has been proposed (for example, in [2, 1, 4]) but there is as yet no common framework in which the extensions can be studied. This seems unfortunate, since in fact the extensions have a great deal in common. In this abstract we consider the problem of defining an assembly language logic for such extensions. The logic should be small and ....

....specification clock b cl are used to arrange that the main minimal fixpoint only has to be unwound if time passes. In a similar style, the timed mu calculus T of [2] with its binary until operator p . q can be translated. As sketched earlier, we can also handle value passing logics such as [1, 4]. The question then is, can we treat in our logic the problems that can be treated in the original logics in particular, the model checking problem both with the generality given by our framework, and in specific domains with the effectiveness of the domain logics. It is easy to see that a ....

J. Rathke, Symbolic Techniques for Value-Passing Calculi. PhD. thesis, University of Sussex, 1997.

....these papers for further discussion of research in this field. This line of work has been the main motivation of this paper, our aim being to extend reasoning about SGA s to handle weak behavioral relations. Definitions of such relations were provided in [6] in the context of the calculus and in [8] for value passing CCS, the latter including symbolic variants. To the best of our knowledge, work involving these equicalences has mainly focused on their characterization [9] The main contributions of this paper can be summarized as follows: First we develop and present algorithms for computing ....

....composition of and oe is the substitution denoted by ; oe such that for every variable x, oe(x) oe( x) oe for ; oe. An SGA is a rooted directed graph where each node n has an associated finite set of free variables fv(n) and each edge is labeled by a guarded action with assignment [3, 8]. Note that a node in SGA is a CCS VP term. Furthermore, we use t to denote the empty action the purpose of which is explained later. Definition 2.1 (SGA) A Symbolic Graph with Assignment (SGA) for CCS VP is a rooted directed graph where each node n has an associated CCS VP term and each edge is ....

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Julian Rathke. Symbolic Techniques for Value-passing Calculi. PhD thesis, University of Sussex, 1997.

....equivalence i which is defined by (t; ffi ) i (t; ffi 0 ) iff ffi and ffi 0 are equal when restricted to the free variables of t. We let p; p 0 range over nodes of T , that is i equivalence classes of pairs [t; ffi ] An important property which relates T to P roc is given in Chapter 2 of [10], namely, if [t; ffi ] 2 T tffi [t; d] An open formulae will require two environments before it can be interpreted: an environment ae : RecV ar ( V ar V al) PT ) which provides a meaning for free recursion variables, and an environment ffi : V ar V al, which provides a meaning for ....

....distinguish non bisimilar processes. Here the only if direction is non trivial because of the presence of fixpoints. Satisfaction of a fixpoint can be considered, semantically, as satisfaction of ordinal unwindings, thus allowing us to proceed by well founded induction. Details can be found in [10]. 2 As a corollary of this we note that because [t; ffi ] tffi we are in fact using a standard interpretation for the logic without tag sets. There now follows a technical Lemma which follows from a generalisation of the so called Reduction Lemma of [14] and simple properties of ....

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J. Rathke. Symbolic techniques for value-passing calculi. PhD thesis, University of Sussex, 1997. To appear.

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J. Rathke. Symbolic Techniques for Value-passing Calculi. Ph.D Thesis, University of Sussex, 1997.

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