Results 1 -
8 of
8
Looking at Mean-Payoff and Total-Payoff through Windows
, 2013
"... We consider two-player games played on weighted directed graphs with mean-payoff and total-payoff objectives, two classical quantitative objectives. While for single-dimensional games the complexity and memory bounds for both objectives coincide, we show that in contrast to multi-dimensional mean-p ..."
Abstract
-
Cited by 3 (0 self)
- Add to MetaCart
We consider two-player games played on weighted directed graphs with mean-payoff and total-payoff objectives, two classical quantitative objectives. While for single-dimensional games the complexity and memory bounds for both objectives coincide, we show that in contrast to multi-dimensional mean-payoff games that are known to be coNP-complete, multi-dimensional total-payoff games are undecidable. We introduce conservative approximations of these objectives, where the payoff is considered over a local finite window sliding along a play, instead of the whole play. For single dimension, we show that (i) if the window size is polynomial, deciding the winner takes polynomial time, and (ii) the existence of a bounded window can be decided in NP ∩ coNP, and is at least as hard as solving mean-payoff games. For multiple dimensions, we show that (i) the problem with fixed window size is EXPTIME-complete, and (ii) there is no primitive-recursive algorithm to decide the existence of a bounded window.
Quantitative verification of weighted Kripke structures
"... Abstract. Extending formal verification techniques to handle quantita-tive aspects, both for the models and for the properties to be checked, has become a central research topic over the last twenty years. Following sev-eral recent works, we study model checking for (one-dimensional) weighted Kripke ..."
Abstract
- Add to MetaCart
(Show Context)
Abstract. Extending formal verification techniques to handle quantita-tive aspects, both for the models and for the properties to be checked, has become a central research topic over the last twenty years. Following sev-eral recent works, we study model checking for (one-dimensional) weighted Kripke structures with positive and negative weights, and temporal logics constraining the total and/or average weight. We prove decidability when only accumulated weight is constrained, while allowing average-weight constraints alone already is undecidable. 1
Symblicit algorithms for optimal strategy synthesis in monotonic Markov decision processes (extended version)?
"... Abstract. When treating Markov decision processes (MDPs) with large state spaces, using explicit representations quickly becomes unfeasible. Lately, Wimmer et al. have proposed a so-called sym-blicit algorithm for the synthesis of optimal strategies in MDPs, in the quantitative setting of expected m ..."
Abstract
- Add to MetaCart
(Show Context)
Abstract. When treating Markov decision processes (MDPs) with large state spaces, using explicit representations quickly becomes unfeasible. Lately, Wimmer et al. have proposed a so-called sym-blicit algorithm for the synthesis of optimal strategies in MDPs, in the quantitative setting of expected mean-payoff. This algorithm, based on the strategy iteration algorithm of Howard and Veinott, effi-ciently combines symbolic and explicit data structures, and uses binary decision diagrams as symbolic representation. The aim of this paper is to show that the new data structure of pseudo-antichains (an extension of antichains) provides another interesting alternative, especially for the class of monotonic MDPs. We design efficient pseudo-antichain based symblicit algorithms (with open source implemen-tations) for two quantitative settings: the expected mean-payoff and the stochastic shortest path. For two practical applications coming from automated planning and LTL synthesis, we report promising experimental results w.r.t. both the run time and the memory consumption. 1
Synthesis from Component Libraries with Costs
"... Abstract. Synthesis is the automated construction of a system from its specifi-cation. In real life, hardware and software systems are rarely constructed from scratch. Rather, a system is typically constructed from a library of components. Lustig and Vardi formalized this intuition and studied LTL s ..."
Abstract
- Add to MetaCart
(Show Context)
Abstract. Synthesis is the automated construction of a system from its specifi-cation. In real life, hardware and software systems are rarely constructed from scratch. Rather, a system is typically constructed from a library of components. Lustig and Vardi formalized this intuition and studied LTL synthesis from com-ponent libraries. In real life, designers seek optimal systems. In this paper we add optimality considerations to the setting. We distinguish between quality consid-erations (for example, size – the smaller a system is, the better it is), and pricing (for example, the payment to the company who manufactured the component). We study the problem of designing systems with minimal quality-cost and price. A key point is that while the quality cost is individual – the choices of a designer are independent of choices made by other designers that use the same library, pricing gives rise to a resource-allocation game – designers that use the same component share its price, with the share being proportional to the number of uses (a component can be used several times in a design). We study both closed and open settings, and in both we solve the problem of finding an optimal design. In a setting with multiple designers, we also study the game-theoretic problems of the induced resource-allocation game. 1
