Satisfiability Games for Branching-Time Logics

The satisfiability problem for branching-time temporal logics like CTL*, CTL and CTL+ has important applications in program specification and verification. Their computational complexities are known: CTL* and CTL+ are complete for doubly exponential time, CTL is complete for single exponential time. Some decision procedures for these logics are known; they use tree automata, tableaux or axiom systems. In this paper we present a uniform game-theoretic framework for the satisfiability problem of these branching-time temporal logics. We define satisfiability games for the full branching-time temporal logic CTL* using a high-level definition of winning condition that captures the essence of well-foundedness of least fixpoint unfoldings. These winning conditions form formal languages of \omega-words. We analyse which kinds of deterministic {\omega}-automata are needed in which case in order to recognise these languages. We then obtain a reduction to the problem of solving parity or B\"uchi games. The worst-case complexity of the obtained algorithms matches the known lower bounds for these logics. This approach provides a uniform, yet complexity-theoretically optimal treatment of satisfiability for branching-time temporal logics. It separates the use of temporal logic machinery from the use of automata thus preserving a syntactical relationship between the input formula and the object that represents satisfiability, i.e. a winning strategy in a parity or B\"uchi game. The games presented here work on a Fischer-Ladner closure of the input formula only. Last but not least, the games presented here come with an attempt at providing tool support for the satisfiability problem of complex branching-time logics like CTL* and CTL+

Automated Game Design Learning

While general game playing is an active field of research, the learning of game design has tended to be either a secondary goal of such research or it has been solely the domain of humans. We propose a field of research, Automated Game Design Learning (AGDL), with the direct purpose of learning game designs directly through interaction with games in the mode that most people experience games: via play. We detail existing work that touches the edges of this field, describe current successful projects in AGDL and the theoretical foundations that enable them, point to promising applications enabled by AGDL, and discuss next steps for this exciting area of study. The key moves of AGDL are to use game programs as the ultimate source of truth about their own design, and to make these design properties available to other systems and avenues of inquiry.Comment: 8 pages, 2 figures. Accepted for CIG 201

How portable is level-0 behavior? A test of level-k theory in game with non-neutral frames

We test the portability of level-0 assumptions in level-k theory in an experimental investigation of behavior in Coordination, Discoordination, and Hide and Seek games with common, non-neutral frames. Assuming that level-0 behavior depends only on the frame, we derive hypotheses that are independent of prior assumptions abou tsalience. Those hypotheses are not confirmed. Our findings contrast with previous research which has fitted parameterized level-k models to Hide and Seek data. We show that, as a criterion of successful explanation, the existence of a plausible model that replicates the main patterns in these data has a high probability of false positives

How can exploratory learning with games and simulations within the curriculum be most effectively evaluated?

There have been few attempts to introduce frameworks that can help support tutors evaluate educational games and simulations that can be most effective in their particular learning context and subject area. The lack of a dedicated framework has produced a significant impediment for uptake of games and simulations particularly in formal learning contexts. This paper aims to address this shortcoming by introducing a four-dimensional framework for helping tutors to evaluate the potential of using games- and simulation- based learning in their practice, and to support more critical approaches to this form of games and simulations. The four-dimensional framework is applied to two examples from practice to test its efficacy and structure critical reflection upon practice

Synthesis of Switching Protocols from Temporal Logic Specifications

We propose formal means for synthesizing switching protocols that determine the sequence in which the modes of a switched system are activated to satisfy certain high-level specifications in linear temporal logic. The synthesized protocols are robust against exogenous disturbances on the continuous dynamics. Two types of finite transition systems, namely under- and over-approximations, that abstract the behavior of the underlying continuous dynamics are defined. In particular, we show that the discrete synthesis problem for an under-approximation can be formulated as a model checking problem, whereas that for an over-approximation can be transformed into a two-player game. Both of these formulations are amenable to efficient, off-the-shelf software tools. By construction, existence of a discrete switching strategy for the discrete synthesis problem guarantees the existence of a continuous switching protocol for the continuous synthesis problem, which can be implemented at the continuous level to ensure the correctness of the nonlinear switched system. Moreover, the proposed framework can be straightforwardly extended to accommodate specifications that require reacting to possibly adversarial external events. Finally, these results are illustrated using three examples from different application domains

Verified Correctness and Security of mbedTLS HMAC-DRBG

We have formalized the functional specification of HMAC-DRBG (NIST 800-90A), and we have proved its cryptographic security--that its output is pseudorandom--using a hybrid game-based proof. We have also proved that the mbedTLS implementation (C program) correctly implements this functional specification. That proof composes with an existing C compiler correctness proof to guarantee, end-to-end, that the machine language program gives strong pseudorandomness. All proofs (hybrid games, C program verification, compiler, and their composition) are machine-checked in the Coq proof assistant. Our proofs are modular: the hybrid game proof holds on any implementation of HMAC-DRBG that satisfies our functional specification. Therefore, our functional specification can serve as a high-assurance reference.Comment: Appearing in CCS '1

Backward Compatibility to Sustain Market Dominance – Evidence from the US Handheld Video Game Industry

The introduction of a new product generation forces incumbents in network industries to rebuild their installed base to maintain an advantage over potential entrants. We study if backward compatibility can help moderate this process of rebuilding an installed base. Using a structural model of the US market for handheld game consoles, we show that backward compatibility lets incumbents transfer network effects from the old generation to the new to some extent but that it also reduces supply of new software. We also find that backward compatibility matters most shortly after the introduction of a new generation. Finally, we examine the tradeoff between technological progress and backward compatibility and find that backward compatibility matters less if there is a large technological leap between two generations. We subsequently use our results to assess the role of backward compatibility as a strategy to sustain a dominant market position