@article{3168,
abstract = {The induction of a signaling pathway is characterized by transient complex formation and mutual posttranslational modification of proteins. To faithfully capture this combinatorial process in a mathematical model is an important challenge in systems biology. Exploiting the limited context on which most binding and modification events are conditioned, attempts have been made to reduce the combinatorial complexity by quotienting the reachable set of molecular species into species aggregates while preserving the deterministic semantics of the thermodynamic limit. Recently, we proposed a quotienting that also preserves the stochastic semantics and that is complete in the sense that the semantics of individual species can be recovered from the aggregate semantics. In this paper, we prove that this quotienting yields a sufficient condition for weak lumpability (that is to say that the quotient system is still Markovian for a given set of initial distributions) and that it gives rise to a backward Markov bisimulation between the original and aggregated transition system (which means that the conditional probability of being in a given state in the original system knowing that we are in its equivalence class is an invariant of the system). We illustrate the framework on a case study of the epidermal growth factor (EGF)/insulin receptor crosstalk.},
author = {Feret, Jérôme and Henzinger, Thomas A and Koeppl, Heinz and Petrov, Tatjana},
journal = {Theoretical Computer Science},
pages = {137 -- 164},
publisher = {Elsevier},
title = {{Lumpability abstractions of rule based systems}},
doi = {10.1016/j.tcs.2011.12.059},
volume = {431},
year = {2012},
}
@article{3846,
abstract = {We summarize classical and recent results about two-player games played on graphs with ω-regular objectives. These games have applications in the verification and synthesis of reactive systems. Important distinctions are whether a graph game is turn-based or concurrent; deterministic or stochastic; zero-sum or not. We cluster known results and open problems according to these classifications.},
author = {Chatterjee, Krishnendu and Henzinger, Thomas A},
journal = {Journal of Computer and System Sciences},
number = {2},
pages = {394 -- 413},
publisher = {Elsevier},
title = {{A survey of stochastic ω regular games}},
doi = {10.1016/j.jcss.2011.05.002},
volume = {78},
year = {2012},
}
@article{2848,
abstract = {We study evolutionary game theory in a setting where individuals learn from each other. We extend the traditional approach by assuming that a population contains individuals with different learning abilities. In particular, we explore the situation where individuals have different search spaces, when attempting to learn the strategies of others. The search space of an individual specifies the set of strategies learnable by that individual. The search space is genetically given and does not change under social evolutionary dynamics. We introduce a general framework and study a specific example in the context of direct reciprocity. For this example, we obtain the counter intuitive result that cooperation can only evolve for intermediate benefit-to-cost ratios, while small and large benefit-to-cost ratios favor defection. Our paper is a step toward making a connection between computational learning theory and evolutionary game dynamics.},
author = {Chatterjee, Krishnendu and Zufferey, Damien and Nowak, Martin},
journal = {Journal of Theoretical Biology},
pages = {161 -- 173},
publisher = {Elsevier},
title = {{Evolutionary game dynamics in populations with different learners}},
doi = {10.1016/j.jtbi.2012.02.021},
volume = {301},
year = {2012},
}
@inproceedings{2956,
abstract = {Two-player games on graphs are central in many problems in formal verification and program analysis such as synthesis and verification of open systems. In this work we consider solving recursive game graphs (or pushdown game graphs) that can model the control flow of sequential programs with recursion. While pushdown games have been studied before with qualitative objectives, such as reachability and parity objectives, in this work we study for the first time such games with the most well-studied quantitative objective, namely, mean payoff objectives. In pushdown games two types of strategies are relevant: (1) global strategies, that depend on the entire global history; and (2) modular strategies, that have only local memory and thus do not depend on the context of invocation, but only on the history of the current invocation of the module. Our main results are as follows: (1) One-player pushdown games with mean-payoff objectives under global strategies are decidable in polynomial time. (2) Two-player pushdown games with mean-payoff objectives under global strategies are undecidable. (3) One-player pushdown games with mean-payoff objectives under modular strategies are NP-hard. (4) Two-player pushdown games with mean-payoff objectives under modular strategies can be solved in NP (i.e., both one-player and two-player pushdown games with mean-payoff objectives under modular strategies are NP-complete). We also establish the optimal strategy complexity showing that global strategies for mean-payoff objectives require infinite memory even in one-player pushdown games; and memoryless modular strategies are sufficient in two-player pushdown games. Finally we also show that all the problems have the same computational complexity if the stack boundedness condition is added, where along with the mean-payoff objective the player must also ensure that the stack height is bounded.},
author = {Chatterjee, Krishnendu and Velner, Yaron},
booktitle = {Proceedings of the 2012 27th Annual ACM/IEEE Symposium on Logic in Computer Science},
location = {Dubrovnik, Croatia },
publisher = {IEEE},
title = {{Mean payoff pushdown games}},
doi = {10.1109/LICS.2012.30},
year = {2012},
}
@inproceedings{3341,
abstract = {We consider two-player stochastic games played on a finite state space for an infinite number of rounds. The games are concurrent: in each round, the two players (player 1 and player 2) choose their moves independently and simultaneously; the current state and the two moves determine a probability distribution over the successor states. We also consider the important special case of turn-based stochastic games where players make moves in turns, rather than concurrently. We study concurrent games with \omega-regular winning conditions specified as parity objectives. The value for player 1 for a parity objective is the maximal probability with which the player can guarantee the satisfaction of the objective against all strategies of the opponent. We study the problem of continuity and robustness of the value function in concurrent and turn-based stochastic parity gameswith respect to imprecision in the transition probabilities. We present quantitative bounds on the difference of the value function (in terms of the imprecision of the transition probabilities) and show the value continuity for structurally equivalent concurrent games (two games are structurally equivalent if the support of the transition function is same and the probabilities differ). We also show robustness of optimal strategies for structurally equivalent turn-based stochastic parity games. Finally we show that the value continuity property breaks without the structurally equivalent assumption (even for Markov chains) and show that our quantitative bound is asymptotically optimal. Hence our results are tight (the assumption is both necessary and sufficient) and optimal (our quantitative bound is asymptotically optimal).},
author = {Chatterjee, Krishnendu},
location = {Tallinn, Estonia},
pages = {270 -- 285},
publisher = {Springer},
title = {{Robustness of structurally equivalent concurrent parity games}},
doi = {10.1007/978-3-642-28729-9_18},
volume = {7213},
year = {2012},
}