Complexity and Approximation Studies of Finding Polynomially Bounded Length Plans for Temporal Goals

Authors

Chitta Baral
Vladik Kreinovich, The University of Texas at El PasoFollow
Sudeshna Sarkar
Nam Tran
Raul Trejo
Xin Zhang

Publication Date

5-2003

Comments

Technical Report: UTEP-CS-01-01f.

Abstract

In this paper, we consider the problem of planning with temporal goals, focussing on polynomially bounded length plans. Past results about complexity of planning are mostly about finding plans that take the world to one of several desired states, often described using a goal formula. We first consider goals expressed using linear temporal logic and analyze the complexity of planning with respect to such goals for both when the states in the trajectory are complete states, and when they are incomplete states. For the later case we also develop a notion of approximate planning and show its complexity to be lower. We also show that this notion of approximate planning is sound. We then consider goals that also have a knowledge component, and refer to such goals as knowledge temporal goals. We analyze the complexity of planning with respect to such goals, propose a notion of approximate planning which is sound and also analyze the complexity of such planning. Finally, we present several goals that can not be adequately expressed using linear temporal logics. To specify these goals, we propose the use of branching time temporal logics such as CTL and CTL*, and define what it means for a plan to satisfy such a goal. We then analyze the complexity of planning with such goals and identify a variant of such goals which leads to a lower complexity of planning.