scholarly journals Programming Combinations of Deduction and BDD-based Symbolic Calculation

2002 ◽  
Vol 5 ◽  
pp. 56-76 ◽  
Author(s):  
Michael J. C. Gordon

AbstractA generalisation of Milner's ‘LCF approach’ is described. This allows algorithms based on binary decision diagrams (BDDs) to be programmed as derived proof rules in a calculus of representation judgements. The derivation of representation judgements becomes an LCF-style proof by defining an abstract type for judgements analogous to the LCF type of theorems. The primitive inference rules for representation judgements correspond to the operations provided by an efficient BDD package coded in C (BuDDy). Proof can combine traditional inference with steps inferring representation judgements. The resulting system provides a platform to support a tight and principled integration of theorem proving and model checking. The methods are illustrated by using them to solve all instances of a generalised Missionaries and Cannibals problem.

2000 ◽  
Vol 13 ◽  
pp. 305-338 ◽  
Author(s):  
A. Cimatti ◽  
M. Roveri

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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