Register-machine based processes

Abstract

We study extensions of the process algebra axiom system ACP with two recursive operations: the binary Kleene star ^*, which is defined by x^*y = x(x^*y + y, and the push-down operation ^$, defined by x^$y = x((x^$y)(x^$y)) + y. In this setting it is easy to represent register machine computation, and an equational theory results that is not decidable. In order to increase the expressive power, abstraction is then added: with rooted branching bisimulation equivalence each computable process can be expressed, and with rooted ô-bisimilarity each semi-computable process that initially is finitely branching can be expressed. Moreover, with abstraction and a finite number of auxiliary actions these results can be obtained without binary Kleene star. Finally, we consider two alternatives for the push-down operation. Each of these gives rise to similar results.

References

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Index Terms

• Computing methodologies

  • Machine learning

    • Machine learning approaches

      • Markov decision processes

  • Symbolic and algebraic manipulation

• Mathematics of computing

  • Continuous mathematics

    • Calculus

  • Probability and statistics

    • Probabilistic representations

      • Decision diagrams

• Software and its engineering

  • Software notations and tools

    • Formal language definitions

• Theory of computation

  • Computational complexity and cryptography

    • Oracles and decision trees

  • Formal languages and automata theory

    • Formalisms

      • Algebraic language theory

  • Logic

  • Models of computation

  • Semantics and reasoning

    • Program reasoning

      • Program specifications

    • Program semantics

      • Algebraic semantics

  • Theory and algorithms for application domains

    • Machine learning theory

      • Markov decision processes

      • Reinforcement learning

        • Sequential decision making