Obligation Blackwell Games and p-Automata

We recently introduced p-automata, automata that read discrete-time Markov chains. We used turn-based stochastic parity games to define acceptance of Markov chains by a subclass of p-automata. Definition of acceptance required a cumbersome and complicated reduction to a series of turn-based stochastic parity games. The reduction could not support acceptance by general p-automata, which was left undefined as there was no notion of games that supported it. Here we generalize two-player games by adding a structural acceptance condition called obligations. Obligations are orthogonal to the linear winning conditions that define winning. Obligations are a declaration that player 0 can achieve a certain value from a configuration. If the obligation is met, the value of that configuration for player 0 is 1. One cannot define value in obligation games by the standard mechanism of considering the measure of winning paths on a Markov chain and taking the supremum of the infimum of all strategies. Mainly because obligations need definition even for Markov chains and the nature of obligations has the flavor of an infinite nesting of supremum and infimum operators. We define value via a reduction to turn-based games similar to Martin's proof of determinacy of Blackwell games with Borel objectives. Based on this definition, we show that games are determined. We show that for Markov chains with Borel objectives and obligations, and finite turn-based stochastic parity games with obligations there exists an alternative and simpler characterization of the value function. Based on this simpler definition we give an exponential time algorithm to analyze finite turn-based stochastic parity games with obligations. Finally, we show that obligation games provide the necessary framework for reasoning about p-automata and that they generalize the previous definition

Measuring the Gain of Reconfigurable Communication

We study the advantages of reconfigurable communication interfaces vs fixed communication interfaces in the context of asynchronous automata. We study the extension of asynchronous (Zielonka) automata with reconfigurable communication interfaces. We show that it is possible to capture languages of automata with reconfigurable communication interfaces by automata with fixed communication interfaces. However, this comes at a cost of disseminating communication (and knowledge) to all agents in a system. Thus, the system is no longer behaving as a distributed system. We then show that this is unavoidable by describing a language in which every agent that uses a fixed communication interface either must be aware of all communication or become irrelevant

Fatal Attractors in Parity Games: Building Blocks for Partial Solvers

Attractors in parity games are a technical device for solving "alternating" reachability of given node sets. A well known solver of parity games - Zielonka's algorithm - uses such attractor computations recursively. We here propose new forms of attractors that are monotone in that they are aware of specific static patterns of colors encountered in reaching a given node set in alternating fashion. Then we demonstrate how these new forms of attractors can be embedded within greatest fixed-point computations to design solvers of parity games that run in polynomial time but are partial in that they may not decide the winning status of all nodes in the input game. Experimental results show that our partial solvers completely solve benchmarks that were constructed to challenge existing full solvers. Our partial solvers also have encouraging run times in practice. For one partial solver we prove that its run-time is at most cubic in the number of nodes in the parity game, that its output game is independent of the order in which monotone attractors are computed, and that it solves all Buechi games and weak games. We then define and study a transformation that converts partial solvers into more precise partial solvers, and we prove that this transformation is sound under very reasonable conditions on the input partial solvers. Noting that one of our partial solvers meets these conditions, we apply its transformation on 1.6 million randomly generated games and so experimentally validate that the transformation can be very effective in increasing the precision of partial solvers

The Rabin index of parity games

We study the descriptive complexity of parity games by taking into account the coloring of their game graphs whilst ignoring their ownership structure. Colored game graphs are identified if they determine the same winning regions and strategies, for all ownership structures of nodes. The Rabin index of a parity game is the minimum of the maximal color taken over all equivalent coloring functions. We show that deciding whether the Rabin index is at least k is in PTIME for k=1 but NP-hard for all fixed k > 1. We present an EXPTIME algorithm that computes the Rabin index by simplifying its input coloring function. When replacing simple cycle with cycle detection in that algorithm, its output over-approximates the Rabin index in polynomial time. Experimental results show that this approximation yields good values in practice.Comment: In Proceedings GandALF 2013, arXiv:1307.416

Linear Temporal Logic for Biologists in BMA

Medical Research Council, Royal SocietyThis is the author accepted manuscript. The final version is available from Springer via http://www.springer.com/in/book/978331945176

A workbench for preprocessor design and evaluation: toward benchmarks for parity games

We describe a prototype workbench for the study of parity games and their solvers. This workbench is aimed at facilitating two activities: to aid in the design, validation, and evaluation of preprocessors for parity game solvers; and to aid in the generation of benchmark parity games that are meaningful for a wide range of solvers. Our workbench allows for easy composition of preprocessors, can populate databases with games and their meta-data, offers a query language for generating games of interest, and has already found potentially hard games

The complexity of global cardinality constraints

In a constraint satisfaction problem (CSP) the goal is to find an assignment of a given set of variables subject to specified constraints. A global cardinality constraint is an additional requirement that prescribes how many variables must be assigned a certain value. We study the complexity of the problem CCSP(G), the constraint satisfaction problem with global cardinality constraints that allows only relations from the set G. The main result of this paper characterizes sets G that give rise to problems solvable in polynomial time, and states that the remaining such problems are NP-complete