566 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 Unifying Approach to Decide Relations for Timed Automata and their Game Characterization
In this paper we present a unifying approach for deciding various
bisimulations, simulation equivalences and preorders between two timed automata
states. We propose a zone based method for deciding these relations in which we
eliminate an explicit product construction of the region graphs or the zone
graphs as in the classical methods. Our method is also generic and can be used
to decide several timed relations. We also present a game characterization for
these timed relations and show that the game hierarchy reflects the hierarchy
of the timed relations. One can obtain an infinite game hierarchy and thus the
game characterization further indicates the possibility of defining new timed
relations which have not been studied yet. The game characterization also helps
us to come up with a formula which encodes the separation between two states
that are not timed bisimilar. Such distinguishing formulae can also be
generated for many relations other than timed bisimilarity.Comment: In Proceedings EXPRESS/SOS 2013, arXiv:1307.690
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
Behavioral Equivalences
Beahvioral equivalences serve to establish in which cases two reactive (possible concurrent) systems offer similar interaction capabilities relatively to other systems representing their operating environment. Behavioral equivalences have been mainly developed in the context
of process algebras, mathematically rigorous languages that have been used for describing and verifying properties of concurrent communicating systems. By relying on the so called structural operational semantics (SOS), labelled transition systems, are associated to each term of a process
algebra. Behavioral equivalences are used to abstract from unwanted details and identify those labelled transition systems that react “similarly” to external experiments. Due to the large number of properties which may be relevant in the analysis of concurrent systems, many different theories
of equivalences have been proposed in the literature. The main contenders consider those systems equivalent that (i) perform the same sequences of actions, or (ii) perform the same sequences of actions and after each sequence are ready to accept the same sets of actions, or (iii) perform the
same sequences of actions and after each sequence exhibit, recursively, the same behavior. This approach leads to many different equivalences that preserve significantly different properties of systems
Forward and Backward Bisimulations for Chemical Reaction Networks
We present two quantitative behavioral equivalences over species of a
chemical reaction network (CRN) with semantics based on ordinary differential
equations. Forward CRN bisimulation identifies a partition where each
equivalence class represents the exact sum of the concentrations of the species
belonging to that class. Backward CRN bisimulation relates species that have
the identical solutions at all time points when starting from the same initial
conditions. Both notions can be checked using only CRN syntactical information,
i.e., by inspection of the set of reactions. We provide a unified algorithm
that computes the coarsest refinement up to our bisimulations in polynomial
time. Further, we give algorithms to compute quotient CRNs induced by a
bisimulation. As an application, we find significant reductions in a number of
models of biological processes from the literature. In two cases we allow the
analysis of benchmark models which would be otherwise intractable due to their
memory requirements.Comment: Extended version of the CONCUR 2015 pape
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
Model-Checking Process Equivalences
Process equivalences are formal methods that relate programs and system
which, informally, behave in the same way. Since there is no unique notion of
what it means for two dynamic systems to display the same behaviour there are a
multitude of formal process equivalences, ranging from bisimulation to trace
equivalence, categorised in the linear-time branching-time spectrum.
We present a logical framework based on an expressive modal fixpoint logic
which is capable of defining many process equivalence relations: for each such
equivalence there is a fixed formula which is satisfied by a pair of processes
if and only if they are equivalent with respect to this relation. We explain
how to do model checking, even symbolically, for a significant fragment of this
logic that captures many process equivalences. This allows model checking
technology to be used for process equivalence checking. We show how partial
evaluation can be used to obtain decision procedures for process equivalences
from the generic model checking scheme.Comment: In Proceedings GandALF 2012, arXiv:1210.202
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
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