Automatic Polytime Reductions of NP Problems into a Fragment of STRIPS

Abstract

We present a software tool that is able to automatically translate an NP problem into a STRIPS problem such that the former problem has a solution iff the latter has one, a solution for the latter can be transformed into a solution for the former, and all this can be done efficiently. Moreover, the tool is built such that it only produces problems that belong to a fragment of STRIPS that is solvable in non-deterministic polynomial time, a fact that guarantees that the whole approach is not an overkill. This tool has interesting applications. For example, with the advancement of planning technology, it can be used as an off-the-shelf method to solve general NP problems with the help of planners and to automatically generate benchmark problems of known complexity in a systematic and controlled manner. Another interesting contribution is related to the area of Knowledge Engineering in which one of the goals is to devise automatic methods for using the available planning technology to solve real-life problems.

Automatic Reductions from PH into STRIPS or How to Generate Short Problems with Very Long Solutions

“…We have extended the tool by Porco, Machado, and Bonet (2011) with a type system and over arbitrary SO formulas which capture the class PH: given such a formula Φ over signature σ and a first-order structure A for σ, the tool generates a planning problem P that has solution iff A Φ. Since problems in PH don't have short certificates in general, the solutions for STRIPS problems generally have exponential length.…”

“…However, SAT-based planners are inherently incomplete when there is no solution, as they continue the search forever unless an upper bound on the length of the plan is given in advance. 2 Porco , Machado, and Bonet (2011) show how to calculate tight lower and upper bounds l(ψ) and u(ψ) on the number of (parallel) actions needed to prove a first-order sentence ψ once the interpretations of the relational symbols occurring in ψ are fixed. We use such estimates to provide tight lower and upper bounds l * (Φ) and u * (Φ) on the length of parallel plans for SO formulas Φ.…”

“…In a recent contribution, Porco, Machado, and Bonet (2011) show how to automatically reduce instances of decision problems in NP into plan-existence decision problems for STRIPS. In this approach, a decision problem Π in NP is encoded as a second-order existential (SO∃) formula Φ, while problem instances are encoded as first-order structures A such that A Φ iff the instance encoded by A belongs to Π.…”

“…Being this a short paper, we don't have the space to present a detailed account of the approach by Porco, Machado, and Bonet (2011). Instead, we revise some known results from Descriptive Complexity, sketch how problems in PH can be automatically translated into STRIPS, and present experimental results.…”

Minimal Landmarks for Optimal Delete-Free Planning

“…An example originating in systems biology is the minimal seed-set problem (Gefen and Brafman 2011), which challenges both classical optimisation methods and optimal planners. Moreover, recent work on translating NP problems into an NP fragment of classical planning opens the possibility that optimal delete-free planning could directly be used to solve a wide range of NP-hard problems (Porco, Machado, and Bonet 2011). Hence practical methods for solving delete-free problems are also important to extend the reach of planning technology.…”