18 research outputs found
2-Nested Simulation is not Finitely Equationally Axiomatizable
2-nested simulation was introduced by Groote and Vaandrager [10] as the coarsest equivalence included in completed trace equivalence for which the tyft/tyxt format is a congruence format. In the lineartime-branching time spectrum of van Glabbeek [8], 2-nested simulationis one of the few equivalences for which no finite equational axiomatization is presented. In this paper we prove that such an axiomatizationdoes not exist for 2-nested simulation.Keywords: Concurrency, process algebra, basic CCS, 2-nested simulation, equational logic, complete axiomatizations
Nested Semantics over Finite Trees are Equationally Hard
This paper studies nested simulation and nested trace semantics over the language BCCSP, a basic formalism to express finite process behaviour. It is shown that none of these semantics affords finite (in)equational axiomatizations over BCCSP. In particular, for each of the nested semantics studied in this paper, the collection of sound, closed (in)equations over a singleton action set is not finitely based
Beyond Language Equivalence on Visibly Pushdown Automata
We study (bi)simulation-like preorder/equivalence checking on the class of
visibly pushdown automata and its natural subclasses visibly BPA (Basic Process
Algebra) and visibly one-counter automata. We describe generic methods for
proving complexity upper and lower bounds for a number of studied preorders and
equivalences like simulation, completed simulation, ready simulation, 2-nested
simulation preorders/equivalences and bisimulation equivalence. Our main
results are that all the mentioned equivalences and preorders are
EXPTIME-complete on visibly pushdown automata, PSPACE-complete on visibly
one-counter automata and P-complete on visibly BPA. Our PSPACE lower bound for
visibly one-counter automata improves also the previously known DP-hardness
results for ordinary one-counter automata and one-counter nets. Finally, we
study regularity checking problems for visibly pushdown automata and show that
they can be decided in polynomial time.Comment: Final version of paper, accepted by LMC
Distances for Weighted Transition Systems: Games and Properties
We develop a general framework for reasoning about distances between
transition systems with quantitative information. Taking as starting point an
arbitrary distance on system traces, we show how this leads to natural
definitions of a linear and a branching distance on states of such a transition
system. We show that our framework generalizes and unifies a large variety of
previously considered system distances, and we develop some general properties
of our distances. We also show that if the trace distance admits a recursive
characterization, then the corresponding branching distance can be obtained as
a least fixed point to a similar recursive characterization. The central tool
in our work is a theory of infinite path-building games with quantitative
objectives.Comment: In Proceedings QAPL 2011, arXiv:1107.074
Continuous Additive Algebras and Injective Simulations of Synchronization Trees
The (in)equational properties of the least fixed point operation on(omega-)continuous functions on (omega-)complete partially ordered sets arecaptured by the axioms of (ordered) iteration algebras, or iterationtheories. We show that the inequational laws of the sum operation inconjunction with the least fixed point operation in continuous additivealgebras have a finite axiomatization over the inequations of orderediteration algebras. As a byproduct of this relative axiomatizability result, we obtain complete infinite inequational and finite implicationalaxiomatizations. Along the way of proving these results, we give a concrete description of the free algebras in the corresponding variety ofordered iteration algebras. This description uses injective simulations of regular synchronization trees. Thus, our axioms are also sound andcomplete for the injective simulation (resource bounded simulation) of(regular) processes.Keywords: equational logic, fixed points, synchronization trees, simulation
Characteristic Formulae for Timed Automata
This paper offers characteristic formula constructions in the real-time logic L for several behavioural relations between (states of)timed automata. The behavioural relations studied in this work aretimed (bi)similarity, timed ready simulation, faster-than bisimilarityand timed trace inclusion. The characteristic formulae delivered byour constructions have size which is linear in that of the timed automaton they logically describe. This also applies to the characteristicformula for timed bisimulation equivalence, for which an exponentialspace construction was previously offered by Laroussinie, Larsen andWeise
On the Existence of a Finite Base for Complete Trace Equivalence over BPA with Interrupt
We study Basic Process Algebra with interrupt modulo complete trace equivalence. We show that, unlike in the setting of the more demanding bisimilarity, a ground complete finite axiomatization exists. We explicitly give such an axiomatization, and extend it to a finite complete one in the special case when a single action is present