Permissive strategies in timed automata and games

Timed automata are a convenient framework for modelling and reasoning about real-time systems. While these models are now well-understood, they do not offer a convenient way of taking timing imprecisions into account. Several solutions (e.g. parametric guard enlargement) have been proposed over the last ten years to take such imprecisions into account. In this paper, we propose a novel approach for handling robust reachability, based on permissive strategies. While classical strategies propose to play an action at an exact point in time, permissive strategies consider intervals of possible dates when to play the selected action. In other words, the controller specifies an interval of time delays for actions to be executed in a more flexible way. With such a permissive strategy, we associate a penalty, which is the inverse of the length of the proposed interval, and accumulates along the run. We show that in that setting, optimal strategies can be computed in polynomial time for one-clock timed automata

Efficient Open World Reasoning for Planning

We consider the problem of reasoning and planning with incomplete knowledge and deterministic actions. We introduce a knowledge representation scheme called PSIPLAN that can effectively represent incompleteness of an agent's knowledge while allowing for sound, complete and tractable entailment in domains where the set of all objects is either unknown or infinite. We present a procedure for state update resulting from taking an action in PSIPLAN that is correct, complete and has only polynomial complexity. State update is performed without considering the set of all possible worlds corresponding to the knowledge state. As a result, planning with PSIPLAN is done without direct manipulation of possible worlds. PSIPLAN representation underlies the PSIPOP planning algorithm that handles quantified goals with or without exceptions that no other domain independent planner has been shown to achieve. PSIPLAN has been implemented in Common Lisp and used in an application on planning in a collaborative interface.Comment: 39 pages, 13 figures. to appear in Logical Methods in Computer Scienc

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

Modeling of Phenomena and Dynamic Logic of Phenomena

Modeling of complex phenomena such as the mind presents tremendous computational complexity challenges. Modeling field theory (MFT) addresses these challenges in a non-traditional way. The main idea behind MFT is to match levels of uncertainty of the model (also, problem or theory) with levels of uncertainty of the evaluation criterion used to identify that model. When a model becomes more certain, then the evaluation criterion is adjusted dynamically to match that change to the model. This process is called the Dynamic Logic of Phenomena (DLP) for model construction and it mimics processes of the mind and natural evolution. This paper provides a formal description of DLP by specifying its syntax, semantics, and reasoning system. We also outline links between DLP and other logical approaches. Computational complexity issues that motivate this work are presented using an example of polynomial models

Metareasoning for Planning Under Uncertainty

The conventional model for online planning under uncertainty assumes that an agent can stop and plan without incurring costs for the time spent planning. However, planning time is not free in most real-world settings. For example, an autonomous drone is subject to nature's forces, like gravity, even while it thinks, and must either pay a price for counteracting these forces to stay in place, or grapple with the state change caused by acquiescing to them. Policy optimization in these settings requires metareasoning---a process that trades off the cost of planning and the potential policy improvement that can be achieved. We formalize and analyze the metareasoning problem for Markov Decision Processes (MDPs). Our work subsumes previously studied special cases of metareasoning and shows that in the general case, metareasoning is at most polynomially harder than solving MDPs with any given algorithm that disregards the cost of thinking. For reasons we discuss, optimal general metareasoning turns out to be impractical, motivating approximations. We present approximate metareasoning procedures which rely on special properties of the BRTDP planning algorithm and explore the effectiveness of our methods on a variety of problems.Comment: Extended version of IJCAI 2015 pape

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