CCS with Hennessy's merge has no finite-equational axiomatization

Abstract This paper confirms a conjecture of Bergstra and Klop¿s from 1984 by establishing that the process algebra obtained by adding an auxiliary operator proposed by Hennessy in 1981 to the recursion free fragment of Milner¿s Calculus of Communicationg Systems is not finitely based modulo bisimulation equivalence. Thus Hennessy¿s merge cannot replace the left merge and communication merge operators proposed by Bergstra and Klop, at least if a finite axiomatization of parallel composition is desired. 2000 MATHEMATICS SUBJECT CLASSIFICATION: 08A70, 03B45, 03C05, 68Q10, 68Q45, 68Q55, 68Q70. CR SUBJECT CLASSIFICATION (1991): D.3.1, F.1.1, F.1.2, F.3.2, F.3.4, F.4.1. KEYWORDS AND PHRASES: Concurrency, process algebra, CCS, bisimulation, Hennessy¿s merge, left merge, communication merge, parallel composition, equational logic, complete axiomatizations, non-finitely based algebras

Logics of Informational Interactions

The pre-eminence of logical dynamics, over a static and purely propositional view of Logic, lies at the core of a new understanding of both formal epistemology and the logical foundations of quantum mechanics. Both areas appear at first sight to be based on purely static propositional formalisms, but in our view their fundamental operators are essentially dynamic in nature. Quantum logic can be best understood as the logic of physically-constrained informational interactions (in the form of measurements and entanglement) between subsystems of a global physical system. Similarly, (multi-agent) epistemic logic is the logic of socially-constrained informational interactions (in the form of direct observations, learning, various forms of communication and testimony) between “subsystems” of a social system. Dynamic Epistemic Logic (DEL) provides us with a unifying setting in which these informational interactions, coming from seemingly very different areas of research, can be fully compared and analyzed. The DEL formalism comes with a powerful set of tools that allows us to make the underlying dynamic/interactive mechanisms fully transparent

On the Axiomatisation of Branching Bisimulation Congruence over CCS

In this paper we investigate the equational theory of (the restriction, relabelling, and recursion free fragment of) CCS modulo rooted branching bisimilarity, which is a classic, bisimulation-based notion of equivalence that abstracts from internal computational steps in process behaviour. Firstly, we show that CCS is not finitely based modulo the considered congruence. As a key step of independent interest in the proof of that negative result, we prove that each CCS process has a unique parallel decomposition into indecomposable processes modulo branching bisimilarity. As a second main contribution, we show that, when the set of actions is finite, rooted branching bisimilarity has a finite equational basis over CCS enriched with the left merge and communication merge operators from ACP

Information-theoretic postulates for quantum theory

Why are the laws of physics formulated in terms of complex Hilbert spaces? Are there natural and consistent modifications of quantum theory that could be tested experimentally? This book chapter gives a self-contained and accessible summary of our paper [New J. Phys. 13, 063001, 2011] addressing these questions, presenting the main ideas, but dropping many technical details. We show that the formalism of quantum theory can be reconstructed from four natural postulates, which do not refer to the mathematical formalism, but only to the information-theoretic content of the physical theory. Our starting point is to assume that there exist physical events (such as measurement outcomes) that happen probabilistically, yielding the mathematical framework of "convex state spaces". Then, quantum theory can be reconstructed by assuming that (i) global states are determined by correlations between local measurements, (ii) systems that carry the same amount of information have equivalent state spaces, (iii) reversible time evolution can map every pure state to every other, and (iv) positivity of probabilities is the only restriction on the possible measurements.Comment: 17 pages, 3 figures. v3: some typos corrected and references updated. Summarizes the argumentation and results of arXiv:1004.1483. Contribution to the book "Quantum Theory: Informational Foundations and Foils", Springer Verlag (http://www.springer.com/us/book/9789401773027), 201

Computing with Capsules

Capsules provide a clean algebraic representation of the state of a computation in higher-order functional and imperative languages. They play the same role as closures or heap- or stack-allocated environments but are much simpler. A capsule is essentially a finite coalgebraic representation of a regular closed lambda-coterm. One can give an operational semantics based on capsules for a higher-order programming language with functional and imperative features, including mutable bindings. Lexical scoping is captured purely algebraically without stacks, heaps, or closures. All operations of interest are typable with simple types, yet the language is Turing complete. Recursive functions are represented directly as capsules without the need for unnatural and untypable fixpoint combinators

Syntactic approaches to negative results in process algebras and modal logics

Concurrency as a phenomenon is observed in most of the current computer science trends. However the inherent complexity of analyzing the behavior of such a system is incremented due to the many different models of concurrency, the variety of applications and architectures, as well as the wide spectrum of specification languages and demanded correctness criteria. For the scope of this thesis we focus on state based models of concurrent computation, and on modal logics as specification languages. First we study syntactically the process algebras that describe several different concurrent behaviors, by analyzing their equational theories. Here, we use well-established techniques from the equational logic of processes to older and newer setups, and then transition to the use of more general and novel methods for the syntactical analysis of models of concurrent programs and specification languages. Our main contributions are several positive and negative axiomatizability results over various process algebraic languages and equivalences, along with some complexity results over the satisfiability of multi-agent modal logic with recursion, as a specification language.Samhliða sem fyrirbæri sést í flestum núverandi tölvunarfræði stefnur. Hins vegar er eðlislægt flókið að greina hegðun slíks kerfis- tem er aukið vegna margra mismunandi gerða samhliða, fjölbreytileikans af forritum og arkitektúr, svo og breitt svið forskrifta mælikvarða og kröfðust réttmætisviðmiða. Fyrir umfang þessarar ritgerðar leggjum við áherslu á ástandsbundin líkön af samhliða útreikningum og á formlegum rökfræði sem forskrift tungumálum. Fyrst skoðum við setningafræðilega ferlialgebrurnar sem lýsa nokkrum mismunandi samhliða hegðun, með því að greina jöfnukenningar þeirra. Hér notum við rótgróin tækni mynda jöfnunarrökfræði ferla til eldri og nýrri uppsetningar, og síðan umskipti yfir í notkun almennari og nýrra aðferða fyrir setningafræðileg greining á líkönum samhliða forrita og forskriftartungumála. Helstu framlög okkar eru nokkrar jákvæðar og neikvæðar niðurstöður um axiomatizability yfir ýmis ferli algebrumál og jafngildi, ásamt nokkrum samSveigjanleiki leiðir af því að fullnægjanleiki fjölþátta formrökfræði með endurkomu, sem a forskrift tungumál.RANNIS: `Open Problems in the Equational Logic of Processes’ (OPEL) (grant No 196050-051) Reykjavik University research fund: `Runtime and Equational Verification of Concurrent Programs' (ReVoCoP) (grant No 222021

Intensional and Extensional Semantics of Bounded and Unbounded Nondeterminism

We give extensional and intensional characterizations of nondeterministic functional programs: as structure preserving functions between biorders, and as nondeterministic sequential algorithms on ordered concrete data structures which compute them. A fundamental result establishes that the extensional and intensional representations of non-deterministic programs are equivalent, by showing how to construct a unique sequential algorithm which computes a given monotone and stable function, and describing the conditions on sequential algorithms which correspond to continuity with respect to each order. We illustrate by defining may and must-testing denotational semantics for a sequential functional language with bounded and unbounded choice operators. We prove that these are computationally adequate, despite the non-continuity of the must-testing semantics of unbounded nondeterminism. In the bounded case, we prove that our continuous models are fully abstract with respect to may and must-testing by identifying a simple universal type, which may also form the basis for models of the untyped lambda-calculus. In the unbounded case we observe that our model contains computable functions which are not denoted by terms, by identifying a further "weak continuity" property of the definable elements, and use this to establish that it is not fully abstract