Axiomatizing GSOS with Predicates (original) (raw)

Proving the validity of equations in GSOS languages using rule-matching bisimilarity

Mathematical Structures in Computer Science, 2012

This paper presents a bisimulation-based method for establishing the soundness of equations between terms constructed using operations whose semantics is specified by rules in the GSOS format of Bloom, Istrail and Meyer. The method is inspired by de Simone's FH-bisimilarity and uses transition rules as schematic transitions in a bisimulation-like relation between open terms. The soundness of the method is proven and examples showing its applicability are provided. The proposed bisimulation-based proof method is incomplete, but the article offers some completeness results for restricted classes of GSOS specifications. An extension of the proof method to the setting of GSOS languages with predicates is also offered.

A bisimulation-based method for proving the validity of equations in GSOS languages

2010

International Journal of Software Science and Computational Intelligence, 2012

The complexity of designing concurrent and highly-evolving interactive systems has grown to a point where system verification has become a hurdle. Fortunately, formal verification methods have arrived at the right time. They detect errors, inconsistencies and incompleteness at early development stages of a system formally modeled using a formal specification language. -calculus (Milner, 1999) is one such formal language which provides strong mathematical base that can be used for verifying system specifications. But manually verifying the specifications of concurrent systems is a very tedious and error-prone work, especially if the specifications are large. Consequently, an automated verification tool would be essential for efficient system design and development. In addition, formal verification tools are vital ingredient to fully harness the potential of component-based software composition. The authors developed such an automated verification tool which is highly portable and sea...

Towards Automatic Bisimilarity Checking in the Spi Calculus

2002

The spi calculus by Abadi and Gordon, an extension of Robin Milner's π-calculus, is designed to model cryptographic protocols. Classic security properties are easily expressed in spi using the notion of testing equivalence by De Nicola and Hennessy. However, proving processes testing equivalent is a daunting task. Thus framed bisimilarity, a bisimulation method implying testing equivalence, has been proposed by Abadi and Gordon. Unfortunately the definition of framed bisimilarity uses several levels of quantification over infinite domains and is therefore not effective. In this paper we define fenced bisimilarity, a concept similar to framed bisimilarity in which one of these quantifiers has been replaced by an effective condition, and show that fenced bisimilarity coincides with framed bisimilarity.

Pointwise extensions of GSOS-defined operations

Mathematical Structures in Computer Science, 2011

Final coalgebras capture system behaviours such as streams, infinite trees and processes. Algebraic operations on a final coalgebra can be defined by distributive laws (of a syntax functor Σ over a behaviour functor F). Such distributive laws correspond to abstract specification formats. One such format is a generalisation of the GSOS rules known from structural operational semantics of processes. We show that given an abstract GSOS specification ρ that defines operations σ on a final F-coalgebra, we can systematically construct a GSOS specification ρ that defines the pointwise extension σ of σ on a final FA-coalgebra. The construction relies on the addition of a family of auxiliary ‘buffer’ operations to the syntax. These buffer operations depend only on A, so the construction is uniform for all σ and F.

Semantics and expressiveness of ordered SOS

Information and Computation, 2009

Structured Operational Semantics (SOS) is a popular method for defining semantics by means of transition rules. An important feature of SOS rules is negative premises, which are crucial in the definitions of such phenomena as priority mechanisms and time-outs. However, the inclusion of negative premises in SOS rules also introduces doubts as to the preferred meaning of SOS specifications.

SOS for Higher Order Processes

2005

We lay the foundations for a Structural Operational Semantics (SOS) framework for higher order processes. Then, we propose a number of extensions to Bernstein’s promoted tyft/tyxt format which aims at proving congruence of strong bisimilarity for higher order processes. The extended format is called promoted PANTH. This format is easier to apply and strictly more expressive than the promoted tyft/tyxt format. Furthermore, we propose and prove a congruence format for a notion of higher order bisimilarity arising naturally from our SOS framework. To illustrate our formats, we apply them to Thomsen’s Calculus of Higher Order Communicating Systems (CHOCS).

Abstract GSOS Rules and a Modular Treatment of Recursive Definitions

Logical Methods in Computer Science, 2013

Terminal coalgebras for a functor serve as semantic domains for state-based systems of various types. For example, behaviors of CCS processes, streams, infinite trees, formal languages and non-well-founded sets form terminal coalgebras. We present a uniform account of the semantics of recursive definitions in terminal coalgebras by combining two ideas: (1) abstract GSOS rules ℓ specify additional algebraic operations on a terminal coalgebra; (2) terminal coalgebras are also initial completely iterative algebras (cias). We also show that an abstract GSOS rule leads to new extended cia structures on the terminal coalgebra. Then we formalize recursive function definitions involving given operations specified by ℓ as recursive program schemes for ℓ, and we prove that unique solutions exist in the extended cias. From our results it follows that the solutions of recursive (function) definitions in terminal coalgebras may be used in subsequent recursive definitions which still have unique solutions. We call this principle modularity. We illustrate our results by the five concrete terminal coalgebras mentioned above, e. g., a finite stream circuit defines a unique stream function.

Axiomatizing GSOS with Predicates (original) (raw)

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