There is increasing awareness that planning and model checking are closely related fields. Abstraction means to perform search in an over-approximation of the original problem instance, with a potentially much smaller...
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There is increasing awareness that planning and model checking are closely related fields. Abstraction means to perform search in an over-approximation of the original problem instance, with a potentially much smaller state space. This is the most essential method in model checking. One would expect that it can also be made successful in planning. We show, however, that this is likely to not be the case. The main reason is that, while in model checking one traditionally uses blind search to exhaust the state space and prove the absence of solutions, in planning informed search is used to find solutions. We give an exhaustive theoretical and practical account of the use of abstraction in planning. For all abstraction (over-approximation) methods known in planning, we prove that they cannot improve the best-case behavior of informed search. While this is easy to see for heuristic search, we were quite surprised to find that it also holds, in most cases, for the resolution-style proofs of unsolvability underlying SAT-based optimal planners. This result is potentially relevant also for model checking, where SAT-based techniques have recently been combined with abstraction. Exploring the issue in planning practice, we find that even hand-made abstractions do not tend to improve the performance of planners, unless the attacked task contains huge amounts of irrelevance. We relate these findings to the kinds of application domains that are typically addressed in model checking.
A new decision procedure for the existential fragment of ordering constraints expressed using the recursive path ordering is presented. This procedure is nondeterministic and checks whether a set of constraints is sol...
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Three different methods for automated geometry theorem proving-a generalized version of Dixon resultants, Gröbner bases and characteristic sets--axe reviewed. The main focus is, however, on the use of the general...
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We show that elementary ACI10 unification is in P, even with constant restrictions. As a corollary, we prove that validity of quantified Horn formulae can be tested in O(n2) time. Solvability of elementary disunificat...
We show that elementary ACI10 unification is in P, even with constant restrictions. As a corollary, we prove that validity of quantified Horn formulae can be tested in O(n2) time. Solvability of elementary disunification problems modulo ACI10 is shown to be NP-hard.
We consider the problem of solving linear equations over various semirings. In particular, solving of linear equations over polynomial rings with the additional restriction that the solutions must have only non-negati...
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We consider the problem of solving linear equations over various semirings. In particular, solving of linear equations over polynomial rings with the additional restriction that the solutions must have only non-negative coefficients is shown to be undecidable. Applications to undecidability proofs of several unification problems are illustrated, one of which, unification modulo one associative-commutative function and one endomorphism, has been a long-standing open problem. The problem of solving multiset constraints is also shown to be undecidable.
For finite convergent term-rewriting systems the equational unification problem is shown to be recursively independent of the equational matching problem, the word matching problem, and the (simultaneous) 2nd-order eq...
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Books on software engineering methodologies talk about the significance and need for designing consistent and complete specifications during the requirement analysis and design stages of a software development cycle. ...
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The concept of anti-link is defined, and useful equivalence-preserving operations on propositional formulas based on anti-links are introduced. These operations eliminate a potentially large number of subsumed paths i...
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Dixon's method for computing multivariate resultants by simultaneously eliminating many variables is reviewed. The method is found to be quite restrictive because often the Dixon matrix is singular, and the Dixon ...
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ISBN:
(纸本)9780897916387
Dixon's method for computing multivariate resultants by simultaneously eliminating many variables is reviewed. The method is found to be quite restrictive because often the Dixon matrix is singular, and the Dixon resultant vanished identically yielding no information about solutions for many algebraic and geometry problems. We extend Dixon's method for the case when the Dixon matrix is singular, but satisfies a condition. An efficient algorithm is developed based on the proposed extension for extracting conditions for the existence of affine solutions of a finite set of polynomials. Using this algorithm, numerous geometric and algebraic identities are derived for examples which appear intractable with other techniques of triangulation such as the successive resultant method, the Gro¨bner basis method, Macaulay resultants and Characteristic set method. Experimental results suggest that the resultant of a set of polynomials which are symmetric in the variables is relatively easier to compute using the extended Dixon's method.
It is shown that unifiability is decidable in theories presented by a set of ground equations with several associative-communicative symbols (ground AC theories). This result applies, for instance, to finitely present...
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It is shown that unifiability is decidable in theories presented by a set of ground equations with several associative-communicative symbols (ground AC theories). This result applies, for instance, to finitely presented commutative semigroups, and it extends the authors' previous work (P. Narendran and M. Rusinwithch, 1991) where they gave an algorithm for solving the uniform word problem in ground AC theories.< >
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