Symbolic model-checking method based on approximations and binary decision diagrams for real-time systems

We tackle the problem of planning in nondeterministic domains, by presenting a new approach to conformant planning. Conformant planning is the problem of finding a sequence of actions that is guaranteed to achieve the goal despite the nondeterminism of the domain. Our approach is based on the representation of the planning domain as a finite state automaton. We use Symbolic Model Checking techniques, in particular Binary Decision Diagrams, to compactly represent and efficiently search the automaton. In this paper we make the following contributions. First, we present a general planning algorithm for conformant planning, which applies to fully nondeterministic domains, with uncertainty in the initial condition and in action effects. The algorithm is based on a breadth-first, backward search, and returns conformant plans of minimal length, if a solution to the planning problem exists, otherwise it terminates concluding that the problem admits no conformant solution. Second, we provide a symbolic representation of the search space based on Binary Decision Diagrams (BDDs), which is the basis for search techniques derived from symbolic model checking. The symbolic representation makes it possible to analyze potentially large sets of states and transitions in a single computation step, thus providing for an efficient implementation. Third, we present CMBP (Conformant Model Based Planner), an efficient implementation of the data structures and algorithm described above, directly based on BDD manipulations, which allows for a compact representation of the search layers and an efficient implementation of the search steps. Finally, we present an experimental comparison of our approach with the state-of-the-art conformant planners CGP, QBFPLAN and GPT. Our analysis includes all the planning problems from the distribution packages of these systems, plus other problems defined to stress a number of specific factors. Our approach appears to be the most effective: CMBP is strictly more expressive than QBFPLAN and CGP and, in all the problems where a comparison is possible, CMBP outperforms its competitors, sometimes by orders of magnitude.

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Compositional and Symbolic Model-Checking of Real-Time Systems

BRICS Report Series ◽

10.7146/brics.v3i59.18770 ◽

1996 ◽

Vol 3 (59) ◽

Cited By ~ 1

Author(s):

Kim G. Larsen ◽

Paul Pettersson ◽

Wang Yi

Keyword(s):

Model Checking ◽

Real Time ◽

Symbolic Model Checking ◽

Automatic Verification ◽

Parallel Composition ◽

Real Time Systems ◽

Symbolic Model ◽

Verification Tools ◽

State Region ◽

Time Systems

Efficient automatic model-checking algorithms for real-time systems have been obtained in recent years based on the state-region graph technique of Alur, Courcoubetis and Dill. However, these algorithms are faced with two potential types of explosion arising from parallel composition: explosion in the space of control nodes, and explosion in the region space over clock variables. In this paper we attack these explosion problems by developing and combining compositional and symbolic model-checking techniques. The presented techniques provide the foundation for a new automatic verification tool Uppaal. Experimental results indicate that Uppaal performs time- and space-wise favorably compared with other real-time verification tools.

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