Tractable constraints in finite semilattices

Rehof, Jakob; Mogensen, Torben Ægidius

doi:10.1007/3-540-61739-6_48

Cited by 35 publications

(38 citation statements)

References 13 publications

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“…The uncertainty can be eliminated by use of quanti er elimination laws [NSC07] to reduce the condition to the following equivalent statement: By applying a constraint propagation algorithm similar to that of Rehof and Mogensen [RM96] we were able to derive an earliest point solution. The solution space could be tightened by applying more sophisticated quanti er elimination methods such as FourierMotzkin or Hodes [Hod71].…”

Section: Reactive Systemsmentioning

confidence: 99%

Theory and Techniques for Synthesizing Efficient Breadth-First Search Algorithms

Nedunuri

Smith

Cook

2012

FM 2012: Formal Methods

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Guided program synthesis is an existing methodology for systematic development of algorithms. Speci c algorithms are viewed as instances of very general algorithm schemas.For example, the Global Search schema generalizes traditional branch-and-bound search, and includes both depth-rst and breadth-rst strategies. Algorithm development involves systematic specialization of the algorithm schema based on problem-speci c constraints to create e cient algorithms that are correct by construction, obviating the need for a separate veri cation step. Guided program synthesis has been applied to a wide range of algorithms, but there is still no systematic process for the synthesis of large search programs such as AI planners.v Our rst contribution is the specialization of Global Search to a class we call E cient Breadth-First Search (EBFS), by incorporating dominance relations to constrain the size of the frontier of the search to be polynomially bounded. Dominance relations allow two search spaces to be compared to determine whether one dominates the other, thus allowing the dominated space to be eliminated from the search. We further show that EBFS is an e ective characterization of greedy algorithms, when the breadth bound is set to one. Surprisingly, the resulting characterization is more general than the well-known characterization of greedy algorithms, namely the Greedy Algorithm parametrized over algebraic structures called greedoids.Our second contribution is a methodology for systematically deriving dominance relations, not just for individual problems but for families of related problems. The techniques are illustrated on numerous well-known problems. Combining this with the program schema for EBFS results in e cient greedy algorithms.Our third contribution is application of the theory and methodology to the practical problem of synthesizing fast planners. Nearly all the state-of-the-art planners in the planning literature are heuristic domain-independent planners. They generally do not scale well and their space requirements also become quite prohibitive. Planners such as TLPlan that incorporate domain-speci c information in the form of control rules are orders of magnitude faster. However, devising the control rules is labor-intensive task and requires domain expertise and insight. The correctness of the rules is also not guaranteed. We introduce a method by which domain-speci c dominance relations can be systematically derived, which can then be turned into control rules, and demonstrate the method on a planning problem (Logistics).vi Many of the derivations are straightforward enough to be automatable.Our third main contribution is showing how to apply the theory and techniqueswe have introduced to a practical problem, namely synthesizing fast AI planners [GNT04].Many of the state-of-the-art planners in the planning literature are domain-independent heuristic planners. They generally do not scale very well and their space requirements also become quite prohibitive. The key to scalable planners is to incorpora...

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Section: Reactive Systemsmentioning

confidence: 99%

Theory and Techniques for Synthesizing Efficient Breadth-First Search Algorithms

Nedunuri

Smith

Cook

2012

FM 2012: Formal Methods

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“…Then, the size of Γ max is linear in the size of G, since for a given κ, the number of types that satisfy θ :: κ is bounded above by a constant. Thus, using Rehof and Mogensen's optimization [21], the above algorithm is made linear in the size of G. The algorithm does not work in practice, however, as the constant factor is too large. Even at the first iteration of the fixedpoint computation, we need to pick each binding F : θ from Γ max and check whether Γ max B R(F ) : θ holds.…”

Section: Examplementioning

confidence: 99%

A Practical Linear Time Algorithm for Trivial Automata Model Checking of Higher-Order Recursion Schemes

Kobayashi

2011

Foundations of Software Science and Computational Structures

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Abstract. The model checking of higher-order recursion schemes has been actively studied and is now becoming a basis of higher-order program verification. We propose a new algorithm for trivial automata model checking of higher-order recursion schemes. To our knowledge, this is the first practical model checking algorithm for recursion schemes that runs in time linear in the size of the higher-order recursion scheme, under the assumption that the size of trivial automata and the largest order and arity of functions are fixed. The previous linear time algorithm was impractical due to a huge constant factor, and the only practical previous algorithm suffers from the hyper-exponential worst-case time complexity, under the same assumption. The new algorithm is remarkably simple, consisting of just two fixed-point computations. We have implemented the algorithm and confirmed that it outperforms Kobayashi's previous algorithm in a certain case.

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“…Therefore, in the above algorithm, both the number of iterations m and the cost for each iteration is O(|G|), so that the algorithm runs in time O(|G| 2 ). By using Rehof and Mogensen's method [30] for solving constraints in finite semi-lattices, we can further optimize it to obtain a linear time algorithm.…”

Section: Type Checking Algorithmmentioning

confidence: 99%

Types and higher-order recursion schemes for verification of higher-order programs

Kobayashi

2009

Proceedings of the 36th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

117

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We propose a new verification method for temporal properties of higher-order functional programs, which takes advantage of Ong's recent result on the decidability of the model-checking problem for higher-order recursion schemes (HORS's). A program is transformed to an HORS that generates a tree representing all the possible event sequences of the program, and then the HORS is modelchecked. Unlike most of the previous methods for verification of higher-order programs, our verification method is sound and complete. Moreover, this new verification framework allows a smooth integration of abstract model checking techniques into verification of higher-order programs. We also present a type-based verification algorithm for HORS's. The algorithm can deal with only a fragment of the properties expressed by modal μ-calculus, but the algorithm and its correctness proof are (arguably) much simpler than those of Ong's game-semantics-based algorithm. Moreover, while the HORS model checking problem is n-EXPTIME in general, our algorithm is linear in the size of HORS, under the assumption that the sizes of types and specifications are bounded by a constant.

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Tractable constraints in finite semilattices

Cited by 35 publications

References 13 publications

Theory and Techniques for Synthesizing Efficient Breadth-First Search Algorithms

Theory and Techniques for Synthesizing Efficient Breadth-First Search Algorithms

A Practical Linear Time Algorithm for Trivial Automata Model Checking of Higher-Order Recursion Schemes

Types and higher-order recursion schemes for verification of higher-order programs

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