1,477 research outputs found
Satisfiability in multi-valued circuits
Satisfiability of Boolean circuits is among the most known and important
problems in theoretical computer science. This problem is NP-complete in
general but becomes polynomial time when restricted either to monotone gates or
linear gates. We go outside Boolean realm and consider circuits built of any
fixed set of gates on an arbitrary large finite domain. From the complexity
point of view this is strictly connected with the problems of solving equations
(or systems of equations) over finite algebras.
The research reported in this work was motivated by a desire to know for
which finite algebras there is a polynomial time algorithm that
decides if an equation over has a solution. We are also looking for
polynomial time algorithms that decide if two circuits over a finite algebra
compute the same function. Although we have not managed to solve these problems
in the most general setting we have obtained such a characterization for a very
broad class of algebras from congruence modular varieties. This class includes
most known and well-studied algebras such as groups, rings, modules (and their
generalizations like quasigroups, loops, near-rings, nonassociative rings, Lie
algebras), lattices (and their extensions like Boolean algebras, Heyting
algebras or other algebras connected with multi-valued logics including
MV-algebras).
This paper seems to be the first systematic study of the computational
complexity of satisfiability of non-Boolean circuits and solving equations over
finite algebras. The characterization results provided by the paper is given in
terms of nice structural properties of algebras for which the problems are
solvable in polynomial time.Comment: 50 page
Split-2 Bisimilarity has a Finite Axiomatization over CCS with<br> Hennessy's Merge
This note shows that split-2 bisimulation equivalence (also known as timed
equivalence) affords a finite equational axiomatization over the process
algebra obtained by adding an auxiliary operation proposed by Hennessy in 1981
to the recursion, relabelling and restriction free fragment of Milner's
Calculus of Communicating Systems. Thus the addition of a single binary
operation, viz. Hennessy's merge, is sufficient for the finite equational
axiomatization of parallel composition modulo this non-interleaving
equivalence. This result is in sharp contrast to a theorem previously obtained
by the same authors to the effect that the same language is not finitely based
modulo bisimulation equivalence
On the Finitary Characterization of pi-Congruences
Some alternative characterizations of late full congruences, either strong or weak, are presented. Those congruences are classically defined by requiring the corresponding ground bisimilarity under all name substitutions. We first improve on those infinitary definitions by showing that congruences can be alternatively characterized in the pi-calculus by sticking to a finitenumber of carefully identified substitutions, and hence, by resorting to only a finite number of ground bisimilarity checks.Then we investigate the same issue in both the ground and the non-ground pi-xsi-calculus, a CCS-like process algebra whose ground version has already been proved to coincide with ground pi-calculus. The pi-xsi-calculus perspective allows processes to be explicitly interpreted as functions of their free names. As aresult, a couple of alternative characterizations of pi-congruences are given, each of them in terms of the bisimilarity of one single pair of pi-xsi-processes. In one case, we exploit lambda-closures of processes, so inducing the effective generationof the substitutions necessary to infer non-ground equivalence. In the other case, a more promising call-by-need discipline for the generation of the wanted substitutions is used. This last strategy is also adopted to show a coincidence result with open semantics. By minor changes, all of the above characterizations for late semantics can be suited for congruences of the early family
Bisimulations for Asynchronous Mobile Processes
Within the past few years there has been renewed interest in thestudy of value-passing process calculi as a consequence of the emergence of the pi-calculus. Here, [MPW89] have determined two variants of the notion of bisimulation, late and early bisimilarity. Most recently [San93] has proposed the new notion of open bisimulation equivalence. In this paper we consider Plain LAL, a mobile process calculus which differs from the pi-calculus in the sense that the communication of data values happens asynchronously. The surprising result is that in the presence of asynchrony, the open, late and early bisimulation equivalences coincide - this in contrast to the pi-calculus where they are distinct. The result allows us to formulate a common equational theory which is sound and complete for finite terms of Plain LAL
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
On the Distributability of Mobile Ambients
Modern society is dependent on distributed software systems and to verify
them different modelling languages such as mobile ambients were developed. To
analyse the quality of mobile ambients as a good foundational model for
distributed computation, we analyse the level of synchronisation between
distributed components that they can express. Therefore, we rely on earlier
established synchronisation patterns. It turns out that mobile ambients are not
fully distributed, because they can express enough synchronisation to express a
synchronisation pattern called M. However, they can express strictly less
synchronisation than the standard pi-calculus. For this reason, we can show
that there is no good and distributability-preserving encoding from the
standard pi-calculus into mobile ambients and also no such encoding from mobile
ambients into the join-calculus, i.e., the expressive power of mobile ambients
is in between these languages. Finally, we discuss how these results can be
used to obtain a fully distributed variant of mobile ambients.Comment: In Proceedings EXPRESS/SOS 2018, arXiv:1808.08071. Conference version
of arXiv:1808.0159
Axiomatizing Prefix Iteration with Silent Steps
Prefix iteration is a variation on the original binary version of the Kleene star operation P*Q, obtained by restricting the first argument to be an atomic action. The interaction of prefix iteration with silent steps is studied in the setting of Milner's basic CCS. Complete equational axiomatizations are given for four notions of behavioural congruence over basic CCS with prefix iteration, viz. branching congruence, eta-congruence, delay congruence and weak congruence. The completeness proofs for eta-, delay, and weak congruence are obtained by reduction to the completeness theorem for branching congruence. It is also argued that the use of the completeness result for branching congruence in obtaining the completeness result for weak congruence leads to a considerable simplification with respect to the only direct proof presented in the literature. The preliminaries and the completeness proofs focus on open terms, i.e. terms that may contain process variables. As a by-product, the omega-completeness of the axiomatizations is obtained as well as their completeness for closed terms. AMS Subject Classification (1991): 68Q10, 68Q40, 68Q55.CR Subject Classification (1991): D.3.1, F.1.2, F.3.2.Keywords and Phrases: Concurrency, process algebra, basic CCS, prefix iteration, branching bisimulation, eta-bisimulation, delay bisimulation, weak bisimulation, equational logic, complete axiomatizations
On bisimulations for the asynchronous π-calculus
AbstractThe asynchronous π-calculus is a variant of the π-calculus where message emission is non-blocking. Honda and Tokoro have studied a semantics for this calculus based on bisimulation. Their bisimulation relies on a modified transition system where, at any moment, a process can perform any input action.In this paper we propose a new notion of bisimulation for the asynchronous π-calculus, defined on top of the standard labelled transition system. We give several characterizations of this equivalence including one in terms of Honda and Tokoro's bisimulation, and one in terms of barbed equivalence. We show that this bisimulation is preserved by name substitutions, hence by input prefix. Finally, we give a complete axiomatization of the (strong) bisimulation for finite terms
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