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Symmetry and Model Checking
, 1994
"... We show how to exploit symmetry in model checking for concurrent systems containing many identical or isomorphic components. We focus in particular on those composed of many isomorphic processes. In many cases we are able to obtain significant, even exponential, savings in the complexity of model ch ..."
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Cited by 166 (15 self)
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We show how to exploit symmetry in model checking for concurrent systems containing many identical or isomorphic components. We focus in particular on those composed of many isomorphic processes. In many cases we are able to obtain significant, even exponential, savings in the complexity of model checking. 1 Introduction In this paper, we show how to exploit symmetry in model checking. We focus on systems composed of many identical (isomorphic) processes. The global state transition graph M of such a system exhibits a great deal of symmetry, characterized by the group of graph automorphisms of M. The basic idea underlying our method is to reduce model checking over the original structure M, to model checking over a smaller quotient structure M, where symmetric states are identified. In the following paragraphs, we give a more detailed but still informal account of a "grouptheoretic" approach to exploiting symmetry. More precisely, the symmetry of M is reflected in the group, Aut M...
An Implementation of Three Algorithms for Timing Verification Based on Automata Emptiness
, 1992
"... This papers describes modifications to and the implementation of algorithms previously described in [1, 11]. We first describe three generic (untimed) algorithms for constructing graphs of the reachable states of a system, and how these graphs can be used for verification. They all have as input an ..."
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Cited by 59 (3 self)
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This papers describes modifications to and the implementation of algorithms previously described in [1, 11]. We first describe three generic (untimed) algorithms for constructing graphs of the reachable states of a system, and how these graphs can be used for verification. They all have as input an implicit description of a transition system. We then apply these algorithms to realtime systems. The first algorithm performs a straightforward reachability analysis on sets of states of the system, rather than on individual states. This corresponds to stepping symbolically through the system many states at a time. In the case of a realtime system this procedure constructs a graph where each node is the union of some regions of the regions graph. There is therefore no need for an a priori partitioning of the state space into individual regions; however, this approach potentially leads to exponentially worse complexity since its potential state space is the power set of regions [1]. The other two algorithms we consider are minimization algorithms [12, 13, 11]. These simultaneously perform reachability analysis and minimization from an implicit system description. These can lead to great savings when the minimized graph is much smaller than the explicit reachable graph. Our paradigm for verification is to test for the emptiness of the set of all timed system executions that violate a requirements specification. One way to specify and verify nonterminating processes is to model them as languages of !sequences of events [14, 15, 16, 1, 17, 18]. Modular processes can be constructed via composition operations involving language intersection. Specifications are also given as languages: they contain all acceptable event sequences. Program correctness is then just language contain...
Incremental Verification by Abstraction
, 2001
"... We present a methodology for constructing abstractions and refining them by analyzing counterexamples. We also present a uniform verification method that combines abstraction, modelchecking and deductive verification in a novel way. In particular, it allows and shows how to use the set of reachabl ..."
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Cited by 29 (3 self)
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We present a methodology for constructing abstractions and refining them by analyzing counterexamples. We also present a uniform verification method that combines abstraction, modelchecking and deductive verification in a novel way. In particular, it allows and shows how to use the set of reachable states of the abstract system in a deductive proof even when the abstract model does not satisfy the specification and when it simulates the concrete system with respect to a weaker simulation notion than Milner's.
Exploiting Structure for Planning and Control
, 1997
"... of " Exploiting Structure for Planning and Control " by ShieuHong Lin, Ph.D., Brown University, May 1997. Thesis advisor Thomas L. Dean. Discrete dynamical systems in the form of finite automata or Markov decision processes have been used as a representational and computational foundation for plann ..."
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Cited by 4 (0 self)
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of " Exploiting Structure for Planning and Control " by ShieuHong Lin, Ph.D., Brown University, May 1997. Thesis advisor Thomas L. Dean. Discrete dynamical systems in the form of finite automata or Markov decision processes have been used as a representational and computational foundation for planning under uncertainty. Many AI planning problems can be conveniently viewed as control problems over the underlying discrete dynamical systems. Using AIstyle representation, the features of application domains are represented as state variables, and planning problem instances compactly encode very large discrete dynamical systems. The standard algorithms to solve the corresponding control problems require explicit enumeration of the underlying state spaces. This is impractical since the sizes of the state spaces are exponential in the number of state variables. In this thesis, we develop decomposition techniques to exploit structure for planning problems in different application domains. Gi...
Abstraction as the Key for Invariant Verification
"... We present a methodology for constructing abstractions and refining them by analyzing counterexamples. We also present a uniform verification method that combines abstraction, modelchecking and deductive verification. In particular, it shows how to use the abstract system in a deductive proof ..."
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Cited by 1 (0 self)
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We present a methodology for constructing abstractions and refining them by analyzing counterexamples. We also present a uniform verification method that combines abstraction, modelchecking and deductive verification. In particular, it shows how to use the abstract system in a deductive proof even when the abstract model does not satisfy the specification and when it simulates the concrete system with respect to a weaker notion of simulation than Milner's.