401 research outputs found
Equivalence-Checking on Infinite-State Systems: Techniques and Results
The paper presents a selection of recently developed and/or used techniques
for equivalence-checking on infinite-state systems, and an up-to-date overview
of existing results (as of September 2004)
A Polynomial Time Algorithm for Deciding Branching Bisimilarity on Totally Normed BPA
Strong bisimilarity on normed BPA is polynomial-time decidable, while weak
bisimilarity on totally normed BPA is NP-hard. It is natural to ask where the
computational complexity of branching bisimilarity on totally normed BPA lies.
This paper confirms that this problem is polynomial-time decidable. To our
knowledge, in the presence of silent transitions, this is the first
bisimilarity checking algorithm on infinite state systems which runs in
polynomial time. This result spots an instance in which branching bisimilarity
and weak bisimilarity are both decidable but lie in different complexity
classes (unless NP=P), which is not known before.
The algorithm takes the partition refinement approach and the final
implementation can be thought of as a generalization of the previous algorithm
of Czerwi\'{n}ski and Lasota. However, unexpectedly, the correctness of the
algorithm cannot be directly generalized from previous works, and the
correctness proof turns out to be subtle. The proof depends on the existence of
a carefully defined refinement operation fitted for our algorithm and the
proposal of elaborately developed techniques, which are quite different from
previous works.Comment: 32 page
Branching Bisimilarity of Normed BPA Processes is in NEXPTIME
Branching bisimilarity on normed BPA processes was recently shown to be
decidable by Yuxi Fu (ICALP 2013) but his proof has not provided any upper
complexity bound. We present a simpler approach based on relative prime
decompositions that leads to a nondeterministic exponential-time algorithm;
this is close to the known exponential-time lower bound.Comment: This is the same text as in July 2014, but only with some
acknowledgment added due to administrative need
Branching Bisimilarity on Normed BPA Is EXPTIME-complete
We put forward an exponential-time algorithm for deciding branching
bisimilarity on normed BPA (Bacis Process Algebra) systems. The decidability of
branching (or weak) bisimilarity on normed BPA was once a long standing open
problem which was closed by Yuxi Fu. The EXPTIME-hardness is an inference of a
slight modification of the reduction presented by Richard Mayr. Our result
claims that this problem is EXPTIME-complete.Comment: We correct many typing errors, add several remarks and an interesting
toy exampl
On the Complexity of Deciding Behavioural Equivalences and Preorders. A Survey
This paper gives an overview of the computational complexity of all the equivalences in the linear/branching time hierarchy [vG90a] and the preordersin the corresponding hierarchy of preorders. We consider finite state or regular processes as well as infinite-state BPA [BK84b] processes. A distinction, which turns out to be important in the finite-state processes, is that of simulation-like equivalences/preorders vs. trace-like equivalencesand preorders. Here we survey various known complexity results for these relations. For regular processes, all simulation-like equivalences and preorders are decidable in polynomial time whereas all trace-like equivalences and preorders are PSPACE-Complete. We also consider interesting specialclasses of regular processes such as deterministic, determinate, unary, locally unary, and tree-like processes and survey the known complexity results inthese special cases. For infinite-state processes the results are quite different. For the class of context-free processes or BPA processes any preorder or equivalence beyond bisimulation is undecidable but bisimulation equivalence is polynomial timedecidable for normed BPA processes and is known to be elementarily decidable in the general case. For the class of BPP processes, all preorders and equivalences apart from bisimilarity are undecidable. However, bisimilarityis decidable in this case and is known to be decidable in polynomial time for normed BPP processes
Bisimilarity of Pushdown Systems is Nonelementary
Given two pushdown systems, the bisimilarity problem asks whether they are
bisimilar. While this problem is known to be decidable our main result states
that it is nonelementary, improving EXPTIME-hardness, which was the previously
best known lower bound for this problem. Our lower bound result holds for
normed pushdown systems as well
Fast equivalence-checking for normed context-free processes
Bisimulation equivalence is decidable in polynomial time over normed graphs generated by a context-free grammar. We present a new algorithm, working in time , thus improving the previously known complexity . It also improves the previously known complexity of the equality problem for simple grammars
Context-Free Session Types for Applied Pi-Calculus
We present a binary session type system using context-free session types to a
version of the applied pi-calculus of Abadi et. al. where only base terms,
constants and channels can be sent. Session types resemble process terms from
BPA and we use a version of bisimulation equivalence to characterize type
equivalence. We present a quotiented type system defined on type equivalence
classes for which type equivalence is built into the type system. Both type
systems satisfy general soundness properties; this is established by an appeal
to a generic session type system for psi-calculi.Comment: In Proceedings EXPRESS/SOS 2018, arXiv:1808.0807
Bisimulation equivalence of a BPP and a finite-state system can be decided in polynomial time
AbstractIn this paper we consider the problem of deciding bisimulation equivalence of a BPP and a finite-state system. We show that the problem can be solved in polynomial time and we present an algorithm deciding the problem in time O(n4). The algorithm also constructs for each state of the finite-state system a ‘symbolic’ semilinear representation of the set of all states of the BPP system which are bisimilar with this state
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