2,036 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)
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
Bisimilarity is not Borel
We prove that the relation of bisimilarity between countable labelled
transition systems is -complete (hence not Borel), by reducing the
set of non-wellorders over the natural numbers continuously to it.
This has an impact on the theory of probabilistic and nondeterministic
processes over uncountable spaces, since logical characterizations of
bisimilarity (as, for instance, those based on the unique structure theorem for
analytic spaces) require a countable logic whose formulas have measurable
semantics. Our reduction shows that such a logic does not exist in the case of
image-infinite processes.Comment: 20 pages, 1 figure; proof of Sigma_1^1 completeness added with
extended comments. I acknowledge careful reading by the referees. Major
changes in Introduction, Conclusion, and motivation for NLMP. Proof for Lemma
22 added, simpler proofs for Lemma 17 and Theorem 30. Added references. Part
of this work was presented at Dagstuhl Seminar 12411 on Coalgebraic Logic
Distribution-based bisimulation for labelled Markov processes
In this paper we propose a (sub)distribution-based bisimulation for labelled
Markov processes and compare it with earlier definitions of state and event
bisimulation, which both only compare states. In contrast to those state-based
bisimulations, our distribution bisimulation is weaker, but corresponds more
closely to linear properties. We construct a logic and a metric to describe our
distribution bisimulation and discuss linearity, continuity and compositional
properties.Comment: Accepted by FORMATS 201
Revisiting bisimilarity and its modal logic for nondeterministic and probabilistic processes
We consider PML, the probabilistic version of Hennessy-Milner logic introduced by Larsen and Skou to characterize bisimilarity over probabilistic processes without internal
nondeterminism.We provide two different interpretations for PML by considering nondeterministic and probabilistic processes as models, and we exhibit two new bisimulation-based equivalences that are in full agreement with those interpretations. Our new equivalences include
as coarsest congruences the two bisimilarities for nondeterministic and probabilistic processes proposed by Segala and Lynch. The latter equivalences are instead in agreement with two versions of Hennessy-Milner logic extended with an additional probabilistic operator
interpreted over state distributions rather than over individual states. Thus, our new interpretations of PML and the corresponding new bisimilarities offer a uniform framework for reasoning on processes that are purely nondeterministic or reactive probabilistic or are mixing nondeterminism and probability in an alternating/non-alternating way
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
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