@inproceedings{2238, abstract = {We study the problem of achieving a given value in Markov decision processes (MDPs) with several independent discounted reward objectives. We consider a generalised version of discounted reward objectives, in which the amount of discounting depends on the states visited and on the objective. This definition extends the usual definition of discounted reward, and allows to capture the systems in which the value of different commodities diminish at different and variable rates. We establish results for two prominent subclasses of the problem, namely state-discount models where the discount factors are only dependent on the state of the MDP (and independent of the objective), and reward-discount models where they are only dependent on the objective (but not on the state of the MDP). For the state-discount models we use a straightforward reduction to expected total reward and show that the problem whether a value is achievable can be solved in polynomial time. For the reward-discount model we show that memory and randomisation of the strategies are required, but nevertheless that the problem is decidable and it is sufficient to consider strategies which after a certain number of steps behave in a memoryless way. For the general case, we show that when restricted to graphs (i.e. MDPs with no randomisation), pure strategies and discount factors of the form 1/n where n is an integer, the problem is in PSPACE and finite memory suffices for achieving a given value. We also show that when the discount factors are not of the form 1/n, the memory required by a strategy can be infinite. }, author = {Chatterjee, Krishnendu and Forejt, Vojtěch and Wojtczak, Dominik}, location = {Stellenbosch, South Africa}, pages = {228 -- 242}, publisher = {Springer}, title = {{Multi-objective discounted reward verification in graphs and MDPs}}, doi = {10.1007/978-3-642-45221-5_17}, volume = {8312}, year = {2013}, } @article{2247, abstract = {Cooperative behavior, where one individual incurs a cost to help another, is a wide spread phenomenon. Here we study direct reciprocity in the context of the alternating Prisoner's Dilemma. We consider all strategies that can be implemented by one and two-state automata. We calculate the payoff matrix of all pairwise encounters in the presence of noise. We explore deterministic selection dynamics with and without mutation. Using different error rates and payoff values, we observe convergence to a small number of distinct equilibria. Two of them are uncooperative strict Nash equilibria representing always-defect (ALLD) and Grim. The third equilibrium is mixed and represents a cooperative alliance of several strategies, dominated by a strategy which we call Forgiver. Forgiver cooperates whenever the opponent has cooperated; it defects once when the opponent has defected, but subsequently Forgiver attempts to re-establish cooperation even if the opponent has defected again. Forgiver is not an evolutionarily stable strategy, but the alliance, which it rules, is asymptotically stable. For a wide range of parameter values the most commonly observed outcome is convergence to the mixed equilibrium, dominated by Forgiver. Our results show that although forgiving might incur a short-term loss it can lead to a long-term gain. Forgiveness facilitates stable cooperation in the presence of exploitation and noise.}, author = {Zagorsky, Benjamin and Reiter, Johannes and Chatterjee, Krishnendu and Nowak, Martin}, journal = {PLoS One}, number = {12}, publisher = {Public Library of Science}, title = {{Forgiver triumphs in alternating prisoner's dilemma }}, doi = {10.1371/journal.pone.0080814}, volume = {8}, year = {2013}, } @inproceedings{2279, abstract = {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.}, author = {Chatterjee, Krishnendu and Doyen, Laurent and Randour, Mickael and Raskin, Jean}, location = {Hanoi, Vietnam}, pages = {118 -- 132}, publisher = {Springer}, title = {{Looking at mean-payoff and total-payoff through windows}}, doi = {10.1007/978-3-319-02444-8_10}, volume = {8172}, year = {2013}, } @proceedings{2292, abstract = {This book constitutes the thoroughly refereed conference proceedings of the 38th International Symposium on Mathematical Foundations of Computer Science, MFCS 2013, held in Klosterneuburg, Austria, in August 2013. The 67 revised full papers presented together with six invited talks were carefully selected from 191 submissions. Topics covered include algorithmic game theory, algorithmic learning theory, algorithms and data structures, automata, formal languages, bioinformatics, complexity, computational geometry, computer-assisted reasoning, concurrency theory, databases and knowledge-based systems, foundations of computing, logic in computer science, models of computation, semantics and verification of programs, and theoretical issues in artificial intelligence.}, editor = {Chatterjee, Krishnendu and Sgall, Jiri}, isbn = {978-3-642-40312-5}, location = {Klosterneuburg, Austria}, pages = {VI -- 854}, publisher = {Springer}, title = {{Mathematical Foundations of Computer Science 2013}}, doi = {10.1007/978-3-642-40313-2}, volume = {8087}, year = {2013}, } @inproceedings{2295, abstract = {We consider partially observable Markov decision processes (POMDPs) with ω-regular conditions specified as parity objectives. The qualitative analysis problem given a POMDP and a parity objective asks whether there is a strategy to ensure that the objective is satisfied with probability 1 (resp. positive probability). While the qualitative analysis problems are known to be undecidable even for very special cases of parity objectives, we establish decidability (with optimal EXPTIME-complete complexity) of the qualitative analysis problems for POMDPs with all parity objectives under finite-memory strategies. We also establish asymptotically optimal (exponential) memory bounds.}, author = {Chatterjee, Krishnendu and Chmelik, Martin and Tracol, Mathieu}, location = {Torino, Italy}, pages = {165 -- 180}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{What is decidable about partially observable Markov decision processes with omega-regular objectives}}, doi = {10.4230/LIPIcs.CSL.2013.165}, volume = {23}, year = {2013}, } @article{2299, abstract = {The standard hardware design flow involves: (a) design of an integrated circuit using a hardware description language, (b) extensive functional and formal verification, and (c) logical synthesis. However, the above-mentioned processes consume significant effort and time. An alternative approach is to use a formal specification language as a high-level hardware description language and synthesize hardware from formal specifications. Our work is a case study of the synthesis of the widely and industrially used AMBA AHB protocol from formal specifications. Bloem et al. presented the first formal specifications for the AMBA AHB Arbiter and synthesized the AHB Arbiter circuit. However, in the first formal specification some important assumptions were missing. Our contributions are as follows: (a) We present detailed formal specifications for the AHB Arbiter incorporating the missing details, and obtain significant improvements in the synthesis results (both with respect to the number of gates in the synthesized circuit and with respect to the time taken to synthesize the circuit), and (b) we present formal specifications to generate compact circuits for the remaining two main components of AMBA AHB, namely, AHB Master and AHB Slave. Thus with systematic description we are able to automatically and completely synthesize an important and widely used industrial protocol.}, author = {Godhal, Yashdeep and Chatterjee, Krishnendu and Henzinger, Thomas A}, journal = {International Journal on Software Tools for Technology Transfer}, number = {5-6}, pages = {585 -- 601}, publisher = {Springer}, title = {{Synthesis of AMBA AHB from formal specification: A case study}}, doi = {10.1007/s10009-011-0207-9}, volume = {15}, year = {2013}, } @inproceedings{2305, abstract = {We study the complexity of central controller synthesis problems for finite-state Markov decision processes, where the objective is to optimize both the expected mean-payoff performance of the system and its stability. e argue that the basic theoretical notion of expressing the stability in terms of the variance of the mean-payoff (called global variance in our paper) is not always sufficient, since it ignores possible instabilities on respective runs. For this reason we propose alernative definitions of stability, which we call local and hybrid variance, and which express how rewards on each run deviate from the run's own mean-payoff and from the expected mean-payoff, respectively. We show that a strategy ensuring both the expected mean-payoff and the variance below given bounds requires randomization and memory, under all the above semantics of variance. We then look at the problem of determining whether there is a such a strategy. For the global variance, we show that the problem is in PSPACE, and that the answer can be approximated in pseudo-polynomial time. For the hybrid variance, the analogous decision problem is in NP, and a polynomial-time approximating algorithm also exists. For local variance, we show that the decision problem is in NP. Since the overall performance can be traded for stability (and vice versa), we also present algorithms for approximating the associated Pareto curve in all the three cases. Finally, we study a special case of the decision problems, where we require a given expected mean-payoff together with zero variance. Here we show that the problems can be all solved in polynomial time.}, author = {Brázdil, Tomáš and Chatterjee, Krishnendu and Forejt, Vojtěch and Kučera, Antonín}, booktitle = {28th Annual ACM/IEEE Symposium}, location = {New Orleans, LA, United States}, pages = {331 -- 340}, publisher = {IEEE}, title = {{Trading performance for stability in Markov decision processes}}, doi = {10.1109/LICS.2013.39}, year = {2013}, } @inproceedings{2329, 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 both finite-state game graphs, and recursive game graphs (or pushdown game graphs) that model the control flow of sequential programs with recursion. The objectives we study are multidimensional mean-payoff objectives, where the goal of player 1 is to ensure that the mean-payoff is non-negative in all dimensions. 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. Our main contributions are as follows: (1) We show that finite-state multidimensional mean-payoff games can be solved in polynomial time if the number of dimensions and the maximal absolute value of the weights are fixed; whereas if the number of dimensions is arbitrary, then the problem is known to be coNP-complete. (2) We show that pushdown graphs with multidimensional mean-payoff objectives can be solved in polynomial time. For both (1) and (2) our algorithms are based on hyperplane separation technique. (3) For pushdown games under global strategies both one and multidimensional mean-payoff objectives problems are known to be undecidable, and we show that under modular strategies the multidimensional problem is also undecidable; under modular strategies the one-dimensional problem is NP-complete. We show that if the number of modules, the number of exits, and the maximal absolute value of the weights are fixed, then pushdown games under modular strategies with one-dimensional mean-payoff objectives can be solved in polynomial time, and if either the number of exits or the number of modules is unbounded, then the problem is NP-hard. (4) Finally we show that a fixed parameter tractable algorithm for finite-state multidimensional mean-payoff games or pushdown games under modular strategies with one-dimensional mean-payoff objectives would imply the fixed parameter tractability of parity games.}, author = {Chatterjee, Krishnendu and Velner, Yaron}, location = {Buenos Aires, Argentinia}, pages = {500 -- 515}, publisher = {Springer}, title = {{Hyperplane separation technique for multidimensional mean-payoff games}}, doi = {10.1007/978-3-642-40184-8_35}, volume = {8052}, year = {2013}, } @inproceedings{2444, abstract = {We consider two core algorithmic problems for probabilistic verification: the maximal end-component decomposition and the almost-sure reachability set computation for Markov decision processes (MDPs). For MDPs with treewidth k, we present two improved static algorithms for both the problems that run in time O(n·k 2.38·2k ) and O(m·logn· k), respectively, where n is the number of states and m is the number of edges, significantly improving the previous known O(n·k·√n· k) bound for low treewidth. We also present decremental algorithms for both problems for MDPs with constant treewidth that run in amortized logarithmic time, which is a huge improvement over the previously known algorithms that require amortized linear time.}, author = {Chatterjee, Krishnendu and Ła̧Cki, Jakub}, location = {St. Petersburg, Russia}, pages = {543 -- 558}, publisher = {Springer}, title = {{Faster algorithms for Markov decision processes with low treewidth}}, doi = {10.1007/978-3-642-39799-8_36}, volume = {8044}, year = {2013}, } @inproceedings{2446, abstract = {The model-checking problem for probabilistic systems crucially relies on the translation of LTL to deterministic Rabin automata (DRW). Our recent Safraless translation [KE12, GKE12] for the LTL(F,G) fragment produces smaller automata as compared to the traditional approach. In this work, instead of DRW we consider deterministic automata with acceptance condition given as disjunction of generalized Rabin pairs (DGRW). The Safraless translation of LTL(F,G) formulas to DGRW results in smaller automata as compared to DRW. We present algorithms for probabilistic model-checking as well as game solving for DGRW conditions. Our new algorithms lead to improvement both in terms of theoretical bounds as well as practical evaluation. We compare PRISM with and without our new translation, and show that the new translation leads to significant improvements.}, author = {Chatterjee, Krishnendu and Gaiser, Andreas and Kretinsky, Jan}, location = {St. Petersburg, Russia}, pages = {559 -- 575}, publisher = {Springer}, title = {{Automata with generalized Rabin pairs for probabilistic model checking and LTL synthesis}}, doi = {10.1007/978-3-642-39799-8_37}, volume = {8044}, year = {2013}, } @article{2814, abstract = {We study the problem of generating a test sequence that achieves maximal coverage for a reactive system under test. We formulate the problem as a repeated game between the tester and the system, where the system state space is partitioned according to some coverage criterion and the objective of the tester is to maximize the set of partitions (or coverage goals) visited during the game. We show the complexity of the maximal coverage problem for non-deterministic systems is PSPACE-complete, but is NP-complete for deterministic systems. For the special case of non-deterministic systems with a re-initializing "reset" action, which represent running a new test input on a re-initialized system, we show that the complexity is coNP-complete. Our proof technique for reset games uses randomized testing strategies that circumvent the exponentially large memory requirement of deterministic testing strategies. We also discuss the memory requirement for deterministic strategies and extensions of our results to other models, such as pushdown systems and timed systems.}, author = {Chatterjee, Krishnendu and Alfaro, Luca and Majumdar, Ritankar}, journal = {International Journal of Foundations of Computer Science}, number = {2}, pages = {165 -- 185}, publisher = {World Scientific Publishing}, title = {{The complexity of coverage}}, doi = {10.1142/S0129054113400066}, volume = {24}, year = {2013}, } @article{2816, abstract = {In solid tumors, targeted treatments can lead to dramatic regressions, but responses are often short-lived because resistant cancer cells arise. The major strategy proposed for overcoming resistance is combination therapy. We present a mathematical model describing the evolutionary dynamics of lesions in response to treatment. We first studied 20 melanoma patients receiving vemurafenib. We then applied our model to an independent set of pancreatic, colorectal, and melanoma cancer patients with metastatic disease. We find that dual therapy results in long-term disease control for most patients, if there are no single mutations that cause cross-resistance to both drugs; in patients with large disease burden, triple therapy is needed. We also find that simultaneous therapy with two drugs is much more effective than sequential therapy. Our results provide realistic expectations for the efficacy of new drug combinations and inform the design of trials for new cancer therapeutics.}, author = {Božić, Ivana and Reiter, Johannes and Allen, Benjamin and Antal, Tibor and Chatterjee, Krishnendu and Shah, Preya and Moon, Yo and Yaqubie, Amin and Kelly, Nicole and Le, Dung and Lipson, Evan and Chapman, Paul and Diaz, Luis and Vogelstein, Bert and Nowak, Martin}, journal = {eLife}, publisher = {eLife Sciences Publications}, title = {{Evolutionary dynamics of cancer in response to targeted combination therapy}}, doi = {10.7554/eLife.00747}, volume = {2}, year = {2013}, } @article{2817, abstract = {The basic idea of evolutionary game theory is that payoff determines reproductive rate. Successful individuals have a higher payoff and produce more offspring. But in evolutionary and ecological situations there is not only reproductive rate but also carrying capacity. Individuals may differ in their exposure to density limiting effects. Here we explore an alternative approach to evolutionary game theory by assuming that the payoff from the game determines the carrying capacity of individual phenotypes. Successful strategies are less affected by density limitation (crowding) and reach higher equilibrium abundance. We demonstrate similarities and differences between our framework and the standard replicator equation. Our equation is defined on the positive orthant, instead of the simplex, but has the same equilibrium points as the replicator equation. Linear stability analysis produces the classical conditions for asymptotic stability of pure strategies, but the stability properties of internal equilibria can differ in the two frameworks. For example, in a two-strategy game with an internal equilibrium that is always stable under the replicator equation, the corresponding equilibrium can be unstable in the new framework resulting in a limit cycle.}, author = {Novak, Sebastian and Chatterjee, Krishnendu and Nowak, Martin}, journal = {Journal of Theoretical Biology}, pages = {26 -- 34}, publisher = {Elsevier}, title = {{Density games}}, doi = {10.1016/j.jtbi.2013.05.029}, volume = {334}, year = {2013}, } @inproceedings{2819, abstract = {We introduce quantatitive timed refinement metrics and quantitative timed simulation functions, incorporating zenoness checks, for timed systems. These functions assign positive real numbers between zero and infinity which quantify the timing mismatches between two timed systems, amongst non-zeno runs. We quantify timing mismatches in three ways: (1) the maximum timing mismatch that can arise, (2) the "steady-state" maximum timing mismatches, where initial transient timing mismatches are ignored; and (3) the (long-run) average timing mismatches amongst two systems. These three kinds of mismatches constitute three important types of timing differences. Our event times are the global times, measured from the start of the system execution, not just the time durations of individual steps. We present algorithms over timed automata for computing the three quantitative simulation functions to within any desired degree of accuracy. In order to compute the values of the quantitative simulation functions, we use a game theoretic formulation. We introduce two new kinds of objectives for two player games on finite state game graphs: (1) eventual debit-sum level objectives, and (2) average debit-sum level objectives. We present algorithms for computing the optimal values for these objectives for player 1, and then use these algorithms to compute the values of the quantitative timed simulation functions. }, author = {Chatterjee, Krishnendu and Prabhu, Vinayak}, booktitle = {Proceedings of the 16th International Conference on Hybrid Systems: Computation and Control}, location = {Philadelphia, PA USA}, pages = {273 -- 282}, publisher = {Springer}, title = {{Quantitative timed simulation functions and refinement metrics for real-time systems}}, doi = {10.1145/2461328.2461370}, volume = {1}, year = {2013}, } @inproceedings{2820, abstract = {In this paper, we introduce the powerful framework of graph games for the analysis of real-time scheduling with firm deadlines. We introduce a novel instance of a partial-observation game that is suitable for this purpose, and prove decidability of all the involved decision problems. We derive a graph game that allows the automated computation of the competitive ratio (along with an optimal witness algorithm for the competitive ratio) and establish an NP-completeness proof for the graph game problem. For a given on-line algorithm, we present polynomial time solution for computing (i) the worst-case utility; (ii) the worst-case utility ratio w.r.t. a clairvoyant off-line algorithm; and (iii) the competitive ratio. A major strength of the proposed approach lies in its flexibility w.r.t. incorporating additional constraints on the adversary and/or the algorithm, including limited maximum or average load, finiteness of periods of overload, etc., which are easily added by means of additional instances of standard objective functions for graph games. }, author = {Chatterjee, Krishnendu and Kößler, Alexander and Schmid, Ulrich}, booktitle = {Proceedings of the 16th International conference on Hybrid systems: Computation and control}, isbn = {978-1-4503-1567-8 }, location = {Philadelphia, PA, United States}, pages = {163 -- 172}, publisher = {ACM}, title = {{Automated analysis of real-time scheduling using graph games}}, doi = {10.1145/2461328.2461356}, year = {2013}, } @article{2824, abstract = {We study synthesis of controllers for real-time systems, where the objective is to stay in a given safe set. The problem is solved by obtaining winning strategies in the setting of concurrent two player timed automaton games with safety objectives. To prevent a player from winning by blocking time, we restrict each player to strategies that ensure that the player cannot be responsible for causing a Zeno run. We construct winning strategies for the controller which require access only to (1) the system clocks (thus, controllers which require their own internal infinitely precise clocks are not necessary), and (2) a logarithmic (in the number of clocks) number of memory bits (i.e. a linear number of memory states). Precisely, we show that for safety objectives, a memory of size (3 + lg (| C | + 1)) bits suffices for winning controller strategies, where C is the set of clocks of the timed automaton game, significantly improving the previous known exponential memory states bound. We also settle the open question of whether winning region-based strategies require memory for safety objectives by showing with an example the necessity of memory for such strategies to win for safety objectives. Finally, we show that the decision problem of determining if there exists a receptive player-1 winning strategy for safety objectives is EXPTIME-complete over timed automaton games.}, author = {Chatterjee, Krishnendu and Prabhu, Vinayak}, journal = {Information and Computation}, pages = {83--119}, publisher = {Elsevier}, title = {{Synthesis of memory-efficient, clock-memory free, and non-Zeno safety controllers for timed systems}}, doi = {10.1016/j.ic.2013.04.003}, volume = {228-229}, year = {2013}, } @article{2831, abstract = {We consider Markov decision processes (MDPs) with Büchi (liveness) objectives. We consider the problem of computing the set of almost-sure winning states from where the objective can be ensured with probability 1. Our contributions are as follows: First, we present the first subquadratic symbolic algorithm to compute the almost-sure winning set for MDPs with Büchi objectives; our algorithm takes O(n · √ m) symbolic steps as compared to the previous known algorithm that takes O(n 2) symbolic steps, where n is the number of states and m is the number of edges of the MDP. In practice MDPs have constant out-degree, and then our symbolic algorithm takes O(n · √ n) symbolic steps, as compared to the previous known O(n 2) symbolic steps algorithm. Second, we present a new algorithm, namely win-lose algorithm, with the following two properties: (a) the algorithm iteratively computes subsets of the almost-sure winning set and its complement, as compared to all previous algorithms that discover the almost-sure winning set upon termination; and (b) requires O(n · √ K) symbolic steps, where K is the maximal number of edges of strongly connected components (scc's) of the MDP. The win-lose algorithm requires symbolic computation of scc's. Third, we improve the algorithm for symbolic scc computation; the previous known algorithm takes linear symbolic steps, and our new algorithm improves the constants associated with the linear number of steps. In the worst case the previous known algorithm takes 5×n symbolic steps, whereas our new algorithm takes 4×n symbolic steps.}, author = {Chatterjee, Krishnendu and Henzinger, Monika H and Joglekar, Manas and Shah, Nisarg}, journal = {Formal Methods in System Design}, number = {3}, pages = {301 -- 327}, publisher = {Springer}, title = {{Symbolic algorithms for qualitative analysis of Markov decision processes with Büchi objectives}}, doi = {10.1007/s10703-012-0180-2}, volume = {42}, year = {2013}, } @article{2836, abstract = {We study the automatic synthesis of fair non-repudiation protocols, a class of fair exchange protocols, used for digital contract signing. First, we show how to specify the objectives of the participating agents and the trusted third party as path formulas in linear temporal logic and prove that the satisfaction of these objectives imply fairness; a property required of fair exchange protocols. We then show that weak (co-operative) co-synthesis and classical (strictly competitive) co-synthesis fail, whereas assume-guarantee synthesis (AGS) succeeds. We demonstrate the success of AGS as follows: (a) any solution of AGS is attack-free; no subset of participants can violate the objectives of the other participants; (b) the Asokan-Shoup-Waidner certified mail protocol that has known vulnerabilities is not a solution of AGS; (c) the Kremer-Markowitch non-repudiation protocol is a solution of AGS; and (d) AGS presents a new and symmetric fair non-repudiation protocol that is attack-free. To our knowledge this is the first application of synthesis to fair non-repudiation protocols, and our results show how synthesis can both automatically discover vulnerabilities in protocols and generate correct protocols. The solution to AGS can be computed efficiently as the secure equilibrium solution of three-player graph games. }, author = {Chatterjee, Krishnendu and Raman, Vishwanath}, journal = {Formal Aspects of Computing}, number = {4}, pages = {825 -- 859}, publisher = {Springer}, title = {{Assume-guarantee synthesis for digital contract signing}}, doi = {10.1007/s00165-013-0283-6}, volume = {26}, year = {2013}, } @article{2854, abstract = {We consider concurrent games played on graphs. At every round of a game, each player simultaneously and independently selects a move; the moves jointly determine the transition to a successor state. Two basic objectives are the safety objective to stay forever in a given set of states, and its dual, the reachability objective to reach a given set of states. First, we present a simple proof of the fact that in concurrent reachability games, for all ε>0, memoryless ε-optimal strategies exist. A memoryless strategy is independent of the history of plays, and an ε-optimal strategy achieves the objective with probability within ε of the value of the game. In contrast to previous proofs of this fact, our proof is more elementary and more combinatorial. Second, we present a strategy-improvement (a.k.a. policy-iteration) algorithm for concurrent games with reachability objectives. Finally, we present a strategy-improvement algorithm for turn-based stochastic games (where each player selects moves in turns) with safety objectives. Our algorithms yield sequences of player-1 strategies which ensure probabilities of winning that converge monotonically (from below) to the value of the game. © 2012 Elsevier Inc.}, author = {Chatterjee, Krishnendu and De Alfaro, Luca and Henzinger, Thomas A}, journal = {Journal of Computer and System Sciences}, number = {5}, pages = {640 -- 657}, publisher = {Elsevier}, title = {{Strategy improvement for concurrent reachability and turn based stochastic safety games}}, doi = {10.1016/j.jcss.2012.12.001}, volume = {79}, year = {2013}, } @article{2858, abstract = {Tumor growth is caused by the acquisition of driver mutations, which enhance the net reproductive rate of cells. Driver mutations may increase cell division, reduce cell death, or allow cells to overcome density-limiting effects. We study the dynamics of tumor growth as one additional driver mutation is acquired. Our models are based on two-type branching processes that terminate in either tumor disappearance or tumor detection. In our first model, both cell types grow exponentially, with a faster rate for cells carrying the additional driver. We find that the additional driver mutation does not affect the survival probability of the lesion, but can substantially reduce the time to reach the detectable size if the lesion is slow growing. In our second model, cells lacking the additional driver cannot exceed a fixed carrying capacity, due to density limitations. In this case, the time to detection depends strongly on this carrying capacity. Our model provides a quantitative framework for studying tumor dynamics during different stages of progression. We observe that early, small lesions need additional drivers, while late stage metastases are only marginally affected by them. These results help to explain why additional driver mutations are typically not detected in fast-growing metastases.}, author = {Reiter, Johannes and Božić, Ivana and Allen, Benjamin and Chatterjee, Krishnendu and Nowak, Martin}, journal = {Evolutionary Applications}, number = {1}, pages = {34 -- 45}, publisher = {Wiley-Blackwell}, title = {{The effect of one additional driver mutation on tumor progression}}, doi = {10.1111/eva.12020}, volume = {6}, year = {2013}, }