On the Complexity of Case-Based Planning

We analyze the computational complexity of problems related to case-based planning: planning when a plan for a similar instance is known, and planning from a library of plans. We prove that planning from a single case has the same complexity than generative planning (i.e., planning "from scratch"); using an extended definition of cases, complexity is reduced if the domain stored in the case is similar to the one to search plans for. Planning from a library of cases is shown to have the same complexity. In both cases, the complexity of planning remains, in the worst case, PSPACE-complete

PDDL: A language with a purpose?

In order to make planning technology more accessible and usable the planning community may have to adopt standard notations for embodying symbolic models of planning domains. In this paper it is argued that before we design such languages for planning we must be able to evaluate their quality. In other words, we must clear for what purpose the languages are to be used, and by what criteria the languages’ effectiveness are to be judged. Here some criteria are set down for languages used for theoretical and practical purposes respectively. PDDL is evaluated with respect to them, with differing results depending on whether PDDL’s purpose is to be a theoretical or practical language. From the results of these evaluations some conclusions are drawn for the development of standard languages for AI planning

OWL-POLAR : A Framework for Semantic Policy Representation and Reasoning

Peer reviewedPreprin

Linear Temporal Logic and Propositional Schemata, Back and Forth (extended version)

This paper relates the well-known Linear Temporal Logic with the logic of propositional schemata introduced by the authors. We prove that LTL is equivalent to a class of schemata in the sense that polynomial-time reductions exist from one logic to the other. Some consequences about complexity are given. We report about first experiments and the consequences about possible improvements in existing implementations are analyzed.Comment: Extended version of a paper submitted at TIME 2011: contains proofs, additional examples & figures, additional comparison between classical LTL/schemata algorithms up to the provided translations, and an example of how to do model checking with schemata; 36 pages, 8 figure

The Complexity of Planning Problems With Simple Causal Graphs

We present three new complexity results for classes of planning problems with simple causal graphs. First, we describe a polynomial-time algorithm that uses macros to generate plans for the class 3S of planning problems with binary state variables and acyclic causal graphs. This implies that plan generation may be tractable even when a planning problem has an exponentially long minimal solution. We also prove that the problem of plan existence for planning problems with multi-valued variables and chain causal graphs is NP-hard. Finally, we show that plan existence for planning problems with binary state variables and polytree causal graphs is NP-complete