Algorithm classification through synthesis

Clark, Keith; Darlington, John

doi:10.1093/comjnl/23.1.61

Cited by 51 publications

(9 citation statements)

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“…In the 70s, Darlington et al [BD77,Dar78,CD80] showed how a family of e cient functional programs for sorting could be derived from both their speci cations and from clearer but less e cient programs, by application of a small set of steps, the best known being fold and unfold. Manna and Waldinger [MW75] carried out similar derivations for imperative programs.…”

Section: Historical Backgroundmentioning

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: Historical Backgroundmentioning

confidence: 99%

Theory and Techniques for Synthesizing Efficient Breadth-First Search Algorithms

Nedunuri

Smith

Cook

2012

FM 2012: Formal Methods

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“…Indeed, it appears that reasoning by analogy may play an important role in the automation of these techniques. Other examples and approaches to program derivation are described in [8], [3], [10], and [4], among others.…”

Section: Combinatorial Lemmas and Program Transformationsmentioning

confidence: 99%

Deriving Efficient Graph Algorithms

Reif

Scherlis

2003

Lecture Notes in Computer Science

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“…In general, by exploring different branches of the proof tree, we may obtain families of different unification algorithms analogous to the families of different sort programs obtained from a single specification by Clark and Darlington [1980]. The particular derivation we obtained did not take the efficiency of the final program into account.…”

Section: Alternate Derivationsmentioning

confidence: 99%