Showing papers by "Jan A. Bergstra published in 2004"

Execution Architectures for Program Algebra

Abstract: We investigate the notion of an execution architecture in the setting of the program algebra PGA, and distinguish two sorts of these: analytic architectures, designed for the purpose of explanation and provided with a process-algebraic, compositional semantics, and synthetic architectures, focusing on how a program may be a physical part of an execution architecture. Then we discuss in detail the Turing machine, a well-known example of an analytic architecture. The logical core of the halting problem — the inability to forecast termination behavior of programs—leads us to a few approaches and examples on related issues: forecasters and rational agents. In particular, we consider architectures suitable to run a Newcomb paradox system and the Prisoner’s Dilemma.

A thread algebra with multi-level strategic interleaving

Abstract: In a previous paper we developed an algebraic theory about threads and a form of concurrency where some deterministic interleaving strategy determines how threads that exist concurrently are interleaved. The interleaving of different threads constitutes a multi-thread. Several multi-threads may exist concurrently on a single host in a network, several host behaviours may exist concurrently in a single network on the internet, etc. In the current paper we assume that the above-mentioned kind of interleaving is also present at those other levels. We extend the theory developed so far with features to cover the multi-level case. We employ the resulting theory to develop a simplified, formal representation schema of the design of systems that consist of several multi-threaded programs on various hosts in different networks and to verify a property of all systems designed according to that schema.

Process algebra for Hybrid systems

Abstract: We propose a process algebra obtained by extending a combination of the process algebra with continuous relative timing from Baeten and Middelburg [Process Algebra with Timing, Springer, Chap. 4, 2002] and the process algebra with propositional signals from Baeten and Bergstra [Theoretical Computer Science 177:381–405, 1997]. The proposed process algebra makes it possible to deal with the behaviour of hybrid systems, i.e. systems in which the instantaneous state transitions caused by performing actions are alternated with continuous state evolutions. This process algebra has, in addition to equational axioms, rules to derive equations with the help of real analysis.

Continuity controlled hybrid automata

Abstract: We investigate the connections between the process algebra for hybrid systems of Bergstra and Middelburg and the formalism of hybrid automata of Henzinger et al. We give interpretations of hybrid automata in the process algebra for hybrid systems and compare them with the standard interpretation of hybrid automata as timed transition systems. We also relate the synchronized product operator on hybrid automata to the parallel composition operator of the process algebra. It turns out that the formalism of hybrid automata matches a fragment of the process algebra for hybrid systems closely. We present an adaptation of the formalism of hybrid automata that yields an exact match.

Machine Function Based Control Code Algebras

Abstract: Machine functions have been introduced by Earley and Sturgis in [6] in order to provide a mathematical foundation of the use of the T-diagrams proposed by Bratman in [5]. Machine functions describe the operation of a machine at a very abstract level. A theory of hardware and software based on machine functions may be called a machine function theory, or alternatively when focusing on inputs and outputs for machine functions a control code algebra (CCA). In this paper we develop some control code algebras from first principles. Machine function types are designed specifically for various application such as program compilation, assembly, interpretation, managed interpretation and just-in-time compilation. Machine function dependent CCA's are used to formalize the well-known compiler fixed point, the managed execution of JIT compiled text and the concept of a verifying compiler.

Machine function based control code algebras

Abstract: Machine functions have been introduced by Earley and Sturgis in [6] in order to provide a mathematical foundation of the use of the T-diagrams proposed by Bratman in [5]. Machine functions describe the operation of a machine at a very abstract level. A theory of hardware and software based on machine functions may be called a machine function theory, or alternatively when focusing on inputs and outputs for machine functions a control code algebra (CCA). In this paper we develop some control code algebras from first principles. Machine function types are designed specifically for various application such as program compilation, assembly, interpretation, managed interpretation and just-in-time compilation. Machine function dependent CCA’s are used to formalize the well-known compiler fixed point, the managed execution of JIT compiled text and the concept of a verifying compiler.

Model Theory for Process Algebra

Abstract: We present a first-order extension of the algebraic theory about processes known as ACP and its main models. Useful predicates on processes, such as deadlock freedom and determinism, can be added to this theory through first-order definitional extensions. Model theory is used to analyse the discrepancies between identity in the models of the first-order extension of ACP and bisimilarity of the transition systems extracted from these models, and also the discrepancies between deadlock freedom in the models of a first-order definitional extension of this theory and deadlock freedom of the transition systems extracted from these models. First-order definitions are material to the formalization of an interpretation of one theory about processes in another. We give a comprehensive example of such an interpretation too.

Linear Projective Program Syntax

Abstract: Based on an extremely simple program notation more advanced program features can be developed in linear projective program syntax such as conditional statements, while loops, recursion, use of an evaluation stack, object classes, method calls etc. Taking care of a cumulative and bottom up introduction of such complex features while providing appropriate projections into the lower levels of language development keeps all definitions rigorous and ensures a clear meaning of higher program constructs.

Continuity Controlled Hybrid Automata

Abstract: We investigate the connections between the process algebra for hybrid systems of Bergstra and Middelburg and the formalism of hybrid automata of Henzinger et al. We give interpretations of hybrid automata in the process algebra for hybrid systems and compare them with the standard interpretation of hybrid automata as timed transition systems. We also relate the synchronized product operator on hybrid automata to the parallel composition operator of the process algebra. It turns out that the formalism of hybrid automata matches a fragment of the process algebra for hybrid systems closely. We present an adaptation of the formalism of hybrid automata that yields an exact match.

Axioms for SNABOK, a System and Network Administration Body of Knowledge: Missing Link Stage of Ontology Process

Abstract: SNABOK, a system an network administration body of knowledge, is coined as an attempt to complement the well-known and quite influential SWEBOK (software engineering body of knowledge) for the less prominent but equally critical profession of system and network administration. General remarks concerning the scope and limits of a SNABOK are discussed and cast in terms of ‘axioms’. Preliminary to a Stoneman, Ironman or Steelman version which should eventually emerge, Missing Link work expresses individual views. SNABOK axiomatization constitutes a part of the Missing Link documentation of SNABOK development.