Complexity, Decidability and Undecidability Results for Domain-Independent Planning: A Detailed Analysis

In this paper, we examine how the complexity of domain-independent planning with STRIPS-like operators depends on the nature of the planning operators. We show conditions under which plannning is decidable and undecidable. Our results on this topic solve an open problem posed by Chapman [4], and clear up some difficulties with his undecidability theorems. For those cases where planning is decidable, we show how the time complexity varies depending on a wide variety of conditions: . whether or not function symbols are allowed; . whether or not delete lists are a]]owed; . whether or not negative preconditions are allowed; . whether or not the predicates are restricted to be propositional(i.e., 0-ary); . whether the planning operators are given as part of the input to the planning prob]em, or instead are fixed in advance. (Also cross-referenced as UMIACS-TR-91-154

Synthesizing and executing plans in Knowledge and Action Bases

We study plan synthesis for a variant of Knowledge and Action Bases (KABs). KABs have been recently introduced as a rich, dynamic framework where states are full-fledged description logic (DL) knowledge bases (KBs) whose extensional part is manipulated by actions that can introduce new objects from an infinite domain. We show that, in general, plan existence over KABs is undecidable even under severe restrictions. We then focus on the class of state-bounded KABs, for which plan existence is decidable, and we provide sound and complete plan synthesis algorithms, through a novel combination of techniques based on standard planning, DL query answering, and finite-state abstractions. All results hold for any DL with decidable query answering. We finally show that for lightweight DLs, plan synthesis can be compiled into standard ADL planning. © 2016, CEUR-WS. All rights reserved

Plan Synthesis for Knowledge and Action Bases

We study plan synthesis for a variant of Knowledge and Action Bases (KABs), a rich, dynamic framework, where states are description logic (DL) knowledge bases (KBs) whose extensional part is manipulated by actions that possibly introduce new objects from an infinite domain. We show that plan existence over KABs is undecidable even under severe restrictions. We then focus on state-bounded KABs, a class for which plan existence is decidable, and provide sound and complete plan synthesis algorithms, which combine techniques based on standard planning, DL query answering, and finite-state abstraction. All results hold for any DL with decidable query answering. We finally show that for lightweight DLs, plan synthesis can be compiled into standard ADL planning

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

A Logic Programming Approach to Knowledge-State Planning: Semantics and Complexity

We propose a new declarative planning language, called K, which is based on principles and methods of logic programming. In this language, transitions between states of knowledge can be described, rather than transitions between completely described states of the world, which makes the language well-suited for planning under incomplete knowledge. Furthermore, it enables the use of default principles in the planning process by supporting negation as failure. Nonetheless, K also supports the representation of transitions between states of the world (i.e., states of complete knowledge) as a special case, which shows that the language is very flexible. As we demonstrate on particular examples, the use of knowledge states may allow for a natural and compact problem representation. We then provide a thorough analysis of the computational complexity of K, and consider different planning problems, including standard planning and secure planning (also known as conformant planning) problems. We show that these problems have different complexities under various restrictions, ranging from NP to NEXPTIME in the propositional case. Our results form the theoretical basis for the DLV^K system, which implements the language K on top of the DLV logic programming system.Comment: 48 pages, appeared as a Technical Report at KBS of the Vienna University of Technology, see http://www.kr.tuwien.ac.at/research/reports

Hybrid conditional planning using answer set programming

We introduce a parallel offline algorithm for computing hybrid conditional plans, called HCP-ASP, oriented towards robotics applications. HCP-ASP relies on modeling actuation actions and sensing actions in an expressive nonmonotonic language of answer set programming (ASP), and computation of the branches of a conditional plan in parallel using an ASP solver. In particular, thanks to external atoms, continuous feasibility checks (like collision checks) are embedded into formal representations of actuation actions and sensing actions in ASP; and thus each branch of a hybrid conditional plan describes a feasible execution of actions to reach their goals. Utilizing nonmonotonic constructs and nondeterministic choices, partial knowledge about states and nondeterministic effects of sensing actions can be explicitly formalized in ASP; and thus each branch of a conditional plan can be computed by an ASP solver without necessitating a conformant planner and an ordering of sensing actions in advance. We apply our method in a service robotics domain and report experimental evaluations. Furthermore, we present performance comparisons with other compilation based conditional planners on standardized benchmark domains

Bounded non-deterministic planning for multimedia adaptation

This paper proposes a novel combination of artificial intelligence planning and other techniques for improving decision-making in the context of multi-step multimedia content adaptation. In particular, it describes a method that allows decision-making (selecting the adaptation to perform) in situations where third-party pluggable multimedia conversion modules are involved and the multimedia adaptation planner does not know their exact adaptation capabilities. In this approach, the multimedia adaptation planner module is only responsible for a part of the required decisions; the pluggable modules make additional decisions based on different criteria. We demonstrate that partial decision-making is not only attainable, but also introduces advantages with respect to a system in which these conversion modules are not capable of providing additional decisions. This means that transferring decisions from the multi-step multimedia adaptation planner to the pluggable conversion modules increases the flexibility of the adaptation. Moreover, by allowing conversion modules to be only partially described, the range of problems that these modules can address increases, while significantly decreasing both the description length of the adaptation capabilities and the planning decision time. Finally, we specify the conditions under which knowing the partial adaptation capabilities of a set of conversion modules will be enough to compute a proper adaptation plan