On the synthesis of a reactive module
POPL '89 Proceedings of the 16th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
On the development of reactive systems
Logics and models of concurrent systems
Reasoning about infinite computations
Information and Computation
Algorithmic mechanism design (extended abstract)
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Automata, Languages, and Machines
Automata, Languages, and Machines
Automata: Theoretic Aspects of Formal Power Series
Automata: Theoretic Aspects of Formal Power Series
Finite-state transducers in language and speech processing
Computational Linguistics
Algorithmic Game Theory
CSL '08 Proceedings of the 22nd international workshop on Computer Science Logic
Reasoning about online algorithms with weighted automata
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Finite automata and their decision problems
IBM Journal of Research and Development
Handbook of Weighted Automata
Quantitative generalizations of languages
DLT'07 Proceedings of the 11th international conference on Developments in language theory
Verifying quantitative properties using bound functions
CHARME'05 Proceedings of the 13 IFIP WG 10.5 international conference on Correct Hardware Design and Verification Methods
TACAS'10 Proceedings of the 16th international conference on Tools and Algorithms for the Construction and Analysis of Systems
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A rational and selfish environment may have an incentive to cheat the system it interacts with. Cheating the system amounts to reporting a stream of inputs that is different from the one corresponding to the real behavior of the environment. The system may cope with cheating by charging penalties to cheats it detects. In this paper, we formalize this setting by means of weighted automata and their resilience to selfish environments. Automata have proven to be a successful formalism for modeling the on-going interaction between a system and its environment. In particular, weighted finite automata (WFAs), which assign a cost to each input word, are useful in modeling an interaction that has a quantitative outcome. Consider a WFA A over the alphabet Σ. At each moment in time, the environment may cheat A by reporting a letter different from the one it actually generates. A penalty function η : Σ × Σ → IR≥0 maps each possible false-report to a penalty, charged whenever the false-report is detected. A detection-probability function p : Σ × Σ → [0, 1] gives the probability of detecting each false-report. We say that A is (η, p)-resilient to cheating if 〈η, p〉 ensures that the minimal expected cost of an input word is achieved with no cheating. Thus, a rational environment has no incentive to cheat A. We study the basic problems arising in the analysis of this setting. In particular, we consider the problem of deciding whether a given WFA A is (η, p)-resilient with respect to a given penalty function η and a detection-probability function p; and the problem of achieving resilience with minimum resources, namely, given A and η, finding the minimal (with respect to Σσ,σ′ η(σ, σ′) ċ p(σ, σ′)) detection-probability function p, such that A is (η, p)-resilient. While for general WFAs both problems are shown to be PSPACE-hard, we present polynomial-time algorithms for deterministic WFAs.