Executable Behaviour and the π-Calculus (extended abstract)

Abstract

Reactive Turing machines extend classical Turing machines with a facility to model observable interactive behaviour. We call a behaviour executable if, and only if, it is behaviourally equivalent to the behaviour of a reactive Turing machine. In this paper, we study the relationship between executable behaviour and behaviour that can be specified in the π-calculus. We establish that all executable behaviour can be specified in the π-calculus up to divergence-preserving branching bisimilarity. The converse, however, is not true due to (intended) limitations of the model of reactive Turing machines. That is, the π-calculus allows the specification of behaviour that is not executable up to divergencepreserving branching bisimilarity. Motivated by an intuitive understanding of executability, we then consider a restriction on the operational semantics of the π-calculus that does associate with every π-term executable behaviour, at least up to the version of branching bisimilarity that does not require the preservation of divergence. * This author is sponsored by the China Scholarship Council (CSC).

On the Executability of Interactive Computation

“…Note that the transition system associated with an RTM/A is boundedly branching. Hence, by Theorem 2 in [12], if a transition system has no divergence up to ↔ ∆ b and is unboundedly branching up to ↔ ∆ b , then it is not executable modulo ↔ ∆ b . It follows that there exist countable unboundedly branching transition systems that cannot be simulated by an RTM/A modulo ↔ ∆ b .…”

On More or Less Appropriate Notions of ‘Computation’

“…Omissions-even of very important papers-in the subsequent paragraphs of this section are thus inevitable. Recently 'trending' topics in this discourse include (Acar, 2012): 'fuzzy' or non-deterministic computing with 'fuzzy' or non-deterministic machines (Li, 2008;Syropoulos, 2016Syropoulos, , 2006, 'infinite-' or 'continuous-time' computing by 'infinite-' or 'continuous-time Turing Machines' (Bournez & Campagnolo, 2008;Hamkins, 2002;Hamkins & Lewis, 2000), 'interactive' (Goldin & Wegner, 2008) or 'reactive' Turing machines (also including: infinite alphabets) (Baeten, Luttik, & Van Tilburg, 2013;Luttik & Yang, 2014 that can communicate or receive 'oracles' (Franchette, 2015;Resconi & Licata, 2012) while running, structurally self-modifying Turing machines (Ramezanian, 2014), 'quantum computing' in which many computations can be super-positioned into one, 'analogue computation' by means of various 'classical' (non-quantum and non-discrete) physical systems (Siegelmann & Sontag, 1994), 'relativistic' computing with the aim of somehow exploiting the space-time effects described by Einstein's theories (Andréka, Németi, & Németi, 2009), 'chemical' and/or 'biological' and/or 'bio-chemical' computing with the aim of using sufficiently complex molecules or living cells or entire organisms as computing devices (Maldonado, Cruz, & Nelson, 2015), as well as 'hybrid' approaches in which any of the previously mentioned ideas can be anyhow mixed and combined: see for example (Syropoulos, 2009). Entire journals and series of conference proceedings are nowadays dedicated to the theme of 'unconventional' computing (International Journal of Unconventional Computing, Unconventional Models of Computation: International Conference Proceedings: Lecture Notes in Computer Science, Workshop Physics and Computation), whereby especially the possibility of 'hyper-computing' (da Costa & Doria, 2006;Hagar & Korolev, 2007;Loff & Costa, 2009;MacLennan, 2009;Teuscher & Sipper, 2002;Wegner & Goldin, 2003)-i.e., being able to decide the classically undecidable Halting Problem effectively and in general by new (whatever 'new' means) devices-has been (and is still being) much contested and debated (in some cases even by naming the opponents)…”

Sequential Composition in the Presence of Intermediate Termination (Extended Abstract)

“…If the standard process algebraic specifications of such memory processes are generalised to a setting with intermediate termination, then either they are not always terminating, or they are 'forgetful' and may non-deterministically lose data. This is a concern when one tries to specify the behaviour of a pushdown automaton or a Reactive Turing machine in a process calculus [5,19,20]. The process calculus TCP with iteration and nesting is Turing complete [11,12].…”