Notion Of Observational Equivalence Research Articles

Prialt in Handel-C: an operational semantics

We describe an operational semantics for the hardware compilation language Handel-C [7], which is a C-like language with channel communication and parallel constructs which compiles down to mainly synchronously clocked hardware. The work in this paper builds on previous work describing the semantics of the "prialt" construct within Handel-C [5] and a denotational semantics for part of the language [6]. We describe a key subset of the language and show how a design decision for the real language, namely that default guards in a prialt statement executed in "zero-time", has consequences for the complexity of the operational semantics. We present the operational semantics, along with a revised and completed prialt semantics, indicating clearly the interface between them. We then describe a notion of observational equivalence and present an example illustrating how we handle the complexity of nested prialts in default guards.

A formal approach for checking security properties in SecSpaces

SecSpaces is a Linda-like coordination model whose aim is to provide a support for secure coordination in Open System applications. Substantially it provides a methodology to restrict the access to the objects stored in the shared dataspace. In this paper we introduce a formal language for representing systems interacting via SecSpaces primitives and its operational semantics. Moreover in this context we consider a notion of observational equivalence, namely testing equivalence. In order to evaluate the adequacy of the model for limiting the access to the shared dataspace, we present some examples of interaction protocols that can be used to obtain some security properties (e.g., authentication or privacy of a datum).

Proof theory of higher-order equations: conservativity, normal forms and term rewriting

We introduce a necessary and sufficient condition for the ω-extensionality rule of higher-order equational logic to be conservative over first-order many-sorted equational logic for ground first-order equations. This gives a precise condition under which computation in the higher-order initial model by term rewriting is possible. The condition is then generalised to characterise a normal form for higher-order equational proofs in which extensionality inferences occur only as the final proof inferences. The main result is based on a notion of observational equivalence between higher-order elements induced by a topology of finite information on such elements. Applied to extensional higher-order algebras with countable first-order carrier sets, the finite information topology is metric and second countable in every type.

Testing monadic code with QuickCheck

QuickCheck is a previously published random testing tool for Haskell programs. In this paper we show how to use it for testing monadic code, and in particular imperative code written using the ST monad. QuickCheck tests a program against a specification: we show that QuickCheck's specification language is sufficiently powerful to represent common forms of specifications: algebraic, model-based (both functional and relational), and pre-/post-conditional. Moreover, all these forms of specification can be used directly for testing. We define a new language of monadic properties, and make a link between program testing and the notion of observational equivalence.

Delay-Insensitivity and Semi-Modularity

The study of asynchronous circuit behaviors in the presence of component and wire delays has received a great deal of attention. In this paper, we consider asynchronous circuits whose components can be any non-deterministic sequential machines of the Moore type, and describe a formal model for these circuits and their behaviors under the inertial delay model. We model an asynchronous circuit C by a network N of modules with delays associated with its components and/or wires. We compute the behavior of N assuming arbitrary inertial delays in the modules, and take this behavior to be correct. We define N to be strongly delay-insensitive if its behavior remains correct in the presence of arbitrary stray delays, where correctness is defined through the notion of observational equivalence (or bisimulation), one of the strongest forms of behavioral equivalence. We introduce the notion of quasi semi-modularity, which generalizes Muller's definition of semi-modularity to non-deterministic networks. We prove that a circuit, with all the wire delays taken into account, is strongly delay-intensitive if and only if its behavior is quasi semi-modular.

An intensional characterization of the largest bisimulation

The notion of observational equivalence in Milner's CCS can be viewed as a limit of finite approximations of P = Q. This limit is however not uniform and is thus perhaps not the intended one. These problems were solved by Park's introduction of the notion of bisimulations. Since the concept of the largest bisimulation is not formulated as a limit, the uniformity ‘missing’ in Milner's observational equivalence is only implicit. In the following note we use proof objects to formulate P = Q explicitly as a uniform limit of finite approximations, which gives an intensional characterization of the largest bisimulation.