32 research outputs found
Decidability and coincidence of equivalences for concurrency
There are two fundamental problems concerning equivalence relations in con-currency. One is: for which system classes is a given equivalence decidable? The second is: when do two equivalences coincide? Two well-known equivalences are history preserving bisimilarity (hpb) and hereditary history preserving bisimi-larity (hhpb). These are both ‘independence ’ equivalences: they reflect causal dependencies between events. Hhpb is obtained from hpb by adding a ‘back-tracking ’ requirement. This seemingly small change makes hhpb computationally far harder: hpb is well-known to be decidable for finite-state systems, whereas the decidability of hhpb has been a renowned open problem for several years; only recently it has been shown undecidable. The main aim of this thesis is to gain insights into the decidability problem for hhpb, and to analyse when it coincides with hpb; less technically, we might say, to analyse the power of the interplay between concurrency, causality, and conflict. We first examine the backtracking condition, and see that it has two dimen
Automata for true concurrency properties
We present an automata-theoretic framework for the model checking of true concurrency properties. These are specified in a fixpoint logic, corresponding to history-preserving bisimilarity, capable of describing events in computations and their dependencies. The models of the logic are event structures or any formalism which can be given a causal semantics, like Petri nets. Given a formula and an event structure satisfying suitable regularity conditions we show how to construct a parity tree automaton whose language is non-empty if and only if the event structure satisfies the formula. The automaton, due to the nature of event structure models, is usually infinite. We discuss how it can be quotiented to an equivalent finite automaton, where emptiness can be checked effectively. In order to show the applicability of the approach, we discuss how it instantiates to finite safe Petri nets. As a proof of concept we provide a model checking tool implementing the technique
History-Preserving Bisimilarity for Higher-Dimensional Automata via Open Maps
We show that history-preserving bisimilarity for higher-dimensional automata
has a simple characterization directly in terms of higher-dimensional
transitions. This implies that it is decidable for finite higher-dimensional
automata. To arrive at our characterization, we apply the open-maps framework
of Joyal, Nielsen and Winskel in the category of unfoldings of precubical sets.Comment: Minor updates in accordance with reviewer comments. Submitted to MFPS
201
(Un)Decidability for History Preserving True Concurrent Logics
We investigate the satisfiability problem for a logic for true concurrency, whose formulae predicate about events in computations and their causal (in)dependencies. Variants of such logics have been studied, with different expressiveness, corresponding to a number of true concurrent behavioural equivalences. Here we focus on a mu-calculus style logic that represents the counterpart of history-preserving (hp-)bisimilarity, a typical equivalence in the true concurrent spectrum of bisimilarities.
It is known that one can decide whether or not two 1-safe Petri nets (and in general finite asynchronous transition systems) are hp-bisimilar. Moreover, for the logic that captures hp-bisimilarity the model-checking problem is decidable with respect to prime event structures satisfying suitable regularity conditions. To the best of our knowledge, the problem of satisfiability has been scarcely investigated in the realm of true concurrent logics.
We show that satisfiability for the logic for hp-bisimilarity is undecidable via a reduction from domino tilings. The fragment of the logic without fixpoints, instead, turns out to be decidable. We consider these results a first step towards a more complete investigation of the satisfiability problem for true concurrent logics, which we believe to have notable solvable cases
On bisimulation and model-checking for concurrent systems with partial order semantics
EP/G012962/1In concurrency theory—the branch of (theoretical) computer science that studies the logical
and mathematical foundations of parallel computation—there are two main formal ways of
modelling the behaviour of systems where multiple actions or events can happen independently
and at the same time: either with interleaving or with partial order semantics.
On the one hand, the interleaving semantics approach proposes to reduce concurrency to the
nondeterministic, sequential computation of the events the system can perform independently.
On the other hand, partial order semantics represent concurrency explicitly by means of an
independence relation on the set of events that the system can execute in parallel; following
this approach, the so-called ‘true concurrency’ approach, independence or concurrency is a
primitive notion rather than a derived concept as in the interleaving framework.
Using interleaving or partial order semantics is, however, more than a matter of taste. In
fact, choosing one kind of semantics over the other can have important implications—both
from theoretical and practical viewpoints—as making such a choice can raise different issues,
some of which we investigate here. More specifically, this thesis studies concurrent systems
with partial order semantics and focuses on their bisimulation and model-checking problems;
the theories and techniques herein apply, in a uniform way, to different classes of Petri nets,
event structures, and transition system with independence (TSI) models.
Some results of this work are: a number of mu-calculi (in this case, fixpoint extensions of
modal logic) that, in certain classes of systems, induce exactly the same identifications as some
of the standard bisimulation equivalences used in concurrency. Secondly, the introduction of
(infinite) higher-order logic games for bisimulation and for model-checking, where the players
of the games are given (local) monadic second-order power on the sets of elements they are
allowed to play. And, finally, the formalization of a new order-theoretic concurrent game
model that provides a uniform approach to bisimulation and model-checking and bridges some
mathematical concepts in order theory with the more operational world of games.
In particular, we show that in all cases the logic games for bisimulation and model-checking
developed in this thesis are sound and complete, and therefore, also determined—even when
considering models of infinite state systems; moreover, these logic games are decidable in the
finite case and underpin novel decision procedures for systems verification.
Since the mu-calculi and (infinite) logic games studied here generalise well-known fixpoint
modal logics as well as game-theoretic decision procedures for analysing concurrent systems
with interleaving semantics, this thesis provides some of the groundwork for the design of a
logic-based, game-theoretic framework for studying, in a uniform manner, several concurrent
systems regardless of whether they have an interleaving or a partial order semantics
Private Names in Non-Commutative Logic
We present an expressive but decidable first-order system (named MAV1) defined by using the calculus of structures, a generalisation of the sequent calculus. In addition to first-order universal and existential quantifiers the system incorporates a de Morgan dual pair of nominal quantifiers called `new\u27 and `wen\u27, distinct from the self-dual Gabbay-Pitts and Miller-Tiu nominal quantifiers. The novelty of the operators `new\u27 and `wen\u27 is they are polarised in the sense that `new\u27 distributes over positive operators while `wen\u27 distributes over negative operators. This greater control of bookkeeping enables private names to be modelled in processes embedded as predicates in MAV1. Modelling processes as predicates in MAV1 has the advantage that linear implication defines a precongruence over processes that fully respects causality and branching. The transitivity of this precongruence is established by novel techniques for handling first-order quantifiers in the cut elimination proof