21 research outputs found
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
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)
Two Lower Bounds for BPA
Branching bisimilarity of normed Basic Process Algebra (nBPA) was claimed to be EXPTIME-hard in previous papers without any explicit proof. Recently it has been pointed out by Petr Jancar that the claim lacked proper justification. In this paper, we develop a new complete proof for the EXPTIME-hardness of branching bisimilarity of nBPA. We also prove that the associated regularity problem of nBPA is PSPACE-hard. This improves previous P-hard result
Game Characterization of Probabilistic Bisimilarity, and Applications to Pushdown Automata
We study the bisimilarity problem for probabilistic pushdown automata (pPDA)
and subclasses thereof. Our definition of pPDA allows both probabilistic and
non-deterministic branching, generalising the classical notion of pushdown
automata (without epsilon-transitions). We first show a general
characterization of probabilistic bisimilarity in terms of two-player games,
which naturally reduces checking bisimilarity of probabilistic labelled
transition systems to checking bisimilarity of standard (non-deterministic)
labelled transition systems. This reduction can be easily implemented in the
framework of pPDA, allowing to use known results for standard
(non-probabilistic) PDA and their subclasses. A direct use of the reduction
incurs an exponential increase of complexity, which does not matter in deriving
decidability of bisimilarity for pPDA due to the non-elementary complexity of
the problem. In the cases of probabilistic one-counter automata (pOCA), of
probabilistic visibly pushdown automata (pvPDA), and of probabilistic basic
process algebras (i.e., single-state pPDA) we show that an implicit use of the
reduction can avoid the complexity increase; we thus get PSPACE, EXPTIME, and
2-EXPTIME upper bounds, respectively, like for the respective non-probabilistic
versions. The bisimilarity problems for OCA and vPDA are known to have matching
lower bounds (thus being PSPACE-complete and EXPTIME-complete, respectively);
we show that these lower bounds also hold for fully probabilistic versions that
do not use non-determinism
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
On the complexity of checking semantic equivalences between pushdown processes and finite-state processes
AbstractSimulation preorder/equivalence and bisimulation equivalence are the most commonly used equivalences in concurrency theory. Their standard definitions are often called strong simulation/bisimulation, while weak simulation/bisimulation abstracts from internal τ-actions.We study the computational complexity of checking these strong and weak semantic preorders/equivalences between pushdown processes and finite-state processes.We present a complete picture of the computational complexity of these problems and also study fixed-parameter tractability in two important input parameters: x, the size of the finite control of the pushdown process, and y, the size of the finite-state process.All simulation problems are generally EXPTIME-complete and only become polynomial if both parameters x and y are fixed.Weak bisimulation equivalence is PSPACE-complete, but becomes polynomial if and only if parameter x is fixed.Strong bisimulation equivalence is PSPACE-complete, but becomes polynomial if either parameter x or y is fixed
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
Resource Bisimilarity in Petri Nets is Decidable
Petri nets are a popular formalism for modeling and analyzing distributed
systems. Tokens in Petri net models can represent the control flow state or
resources produced/consumed by transition firings. We define a resource as a
part (submultiset) of the Petri net marking and call two resources equivalent
iff replacing one of them with another in any marking does not change the
observable Petri net behavior. We investigate the resource similarity and the
resource bisimilarity -- congruent restrictions of the bisimulation equivalence
on Petri net markings and prove that the resource bisimilarity is decidable in
contrast to the resource similarity.Comment: New version for submission to the journa