TY - CONF
AB - The importance of stochasticity within biological systems has been shown repeatedly during the last years and has raised the need for efficient stochastic tools. We present SABRE, a tool for stochastic analysis of biochemical reaction networks. SABRE implements fast adaptive uniformization (FAU), a direct numerical approximation algorithm for computing transient solutions of biochemical reaction networks. Biochemical reactions networks represent biological systems studied at a molecular level and these reactions can be modeled as transitions of a Markov chain. SABRE accepts as input the formalism of guarded commands, which it interprets either as continuous-time or as discrete-time Markov chains. Besides operating in a stochastic mode, SABRE may also perform a deterministic analysis by directly computing a mean-field approximation of the system under study. We illustrate the different functionalities of SABRE by means of biological case studies.
AU - Didier, Frédéric
AU - Henzinger, Thomas A
AU - Mateescu, Maria
AU - Wolf, Verena
ID - 3847
TI - SABRE: A tool for the stochastic analysis of biochemical reaction networks
ER -
TY - CONF
AB - Using ideas from persistent homology, the robustness of a level set of a real-valued function is defined in terms of the magnitude of the perturbation necessary to kill the classes. Prior work has shown that the homology and robustness information can be read off the extended persistence diagram of the function. This paper extends these results to a non-uniform error model in which perturbations vary in their magnitude across the domain.
AU - Bendich, Paul
AU - Edelsbrunner, Herbert
AU - Kerber, Michael
AU - Patel, Amit
ID - 3849
TI - Persistent homology under non-uniform error
VL - 6281
ER -
TY - JOUR
AB - Scanning tunneling spectroscopy studies on high-quality Bi2Te3 crystals exhibit perfect correspondence to angle-resolved photoemission spectroscopy data, hence enabling identification of different regimes measured in the local density of states (LDOS). Oscillations of LDOS near a step are analyzed. Within the main part of the surface band oscillations are strongly damped, supporting the hypothesis of topological protection. At higher energies, as the surface band becomes concave, oscillations appear, dispersing with a wave vector that may result from a hexagonal warping term.
AU - Alpichshev, Zhanybek
AU - Analytis, James
AU - Chu, Jiunhaw
AU - Fisher, Ian
AU - Chen, Yulin
AU - Shen, Zhixun
AU - Fang, Aiping
AU - Kapitulnik, Aharon
ID - 385
IS - 1
JF - Physical Review Letters
TI - STM imaging of electronic waves on the surface of Bi2Te3 Topologically protected surface states and hexagonal warping effects
VL - 104
ER -
TY - CONF
AB - Energy parity games are infinite two-player turn-based games played on weighted graphs. The objective of the game combines a (qualitative) parity condition with the (quantitative) requirement that the sum of the weights (i.e., the level of energy in the game) must remain positive. Beside their own interest in the design and synthesis of resource-constrained omega-regular specifications, energy parity games provide one of the simplest model of games with combined qualitative and quantitative objective. Our main results are as follows: (a) exponential memory is sufficient and may be necessary for winning strategies in energy parity games; (b) the problem of deciding the winner in energy parity games can be solved in NP ∩ coNP; and (c) we give an algorithm to solve energy parity by reduction to energy games. We also show that the problem of deciding the winner in energy parity games is polynomially equivalent to the problem of deciding the winner in mean-payoff parity games, which can thus be solved in NP ∩ coNP. As a consequence we also obtain a conceptually simple algorithm to solve mean-payoff parity games.
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
ID - 3851
TI - Energy parity games
VL - 6199
ER -
TY - CONF
AB - We introduce two-level discounted games played by two players on a perfect-information stochastic game graph. The upper level game is a discounted game and the lower level game is an undiscounted reachability game. Two-level games model hierarchical and sequential decision making under uncertainty across different time scales. We show the existence of pure memoryless optimal strategies for both players and an ordered field property for such games. We show that if there is only one player (Markov decision processes), then the values can be computed in polynomial time. It follows that whether the value of a player is equal to a given rational constant in two-level discounted games can be decided in NP intersected coNP. We also give an alternate strategy improvement algorithm to compute the value.
AU - Chatterjee, Krishnendu
AU - Majumdar, Ritankar
ID - 3852
TI - Discounting in games across time scales
VL - 25
ER -
TY - CONF
AB - Quantitative languages are an extension of boolean languages that assign to each word a real number. Mean-payoff automata are finite automata with numerical weights on transitions that assign to each infinite path the long-run average of the transition weights. When the mode of branching of the automaton is deterministic, nondeterministic, or alternating, the corresponding class of quantitative languages is not robust as it is not closed under the pointwise operations of max, min, sum, and numerical complement. Nondeterministic and alternating mean-payoff automata are not decidable either, as the quantitative generalization of the problems of universality and language inclusion is undecidable. We introduce a new class of quantitative languages, defined by mean-payoff automaton expressions, which is robust and decidable: it is closed under the four pointwise operations, and we show that all decision problems are decidable for this class. Mean-payoff automaton expressions subsume deterministic meanpayoff automata, and we show that they have expressive power incomparable to nondeterministic and alternating mean-payoff automata. We also present for the first time an algorithm to compute distance between two quantitative languages, and in our case the quantitative languages are given as mean-payoff automaton expressions.
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
AU - Edelsbrunner, Herbert
AU - Henzinger, Thomas A
AU - Rannou, Philippe
ID - 3853
TI - Mean-payoff automaton expressions
VL - 6269
ER -
TY - CONF
AB - We study observation-based strategies for partially-observable Markov decision processes (POMDPs) with parity objectives. An observation-based strategy relies on partial information about the history of a play, namely, on the past sequence of observations. We consider qualitative analysis problems: given a POMDP with a parity objective, decide whether there exists an observation-based strategy to achieve the objective with probability 1 (almost-sure winning), or with positive probability (positive winning). Our main results are twofold. First, we present a complete picture of the computational complexity of the qualitative analysis problem for POMDPs with parity objectives and its subclasses: safety, reachability, Büchi, and coBüchi objectives. We establish several upper and lower bounds that were not known in the literature. Second, we give optimal bounds (matching upper and lower bounds) for the memory required by pure and randomized observation-based strategies for each class of objectives.
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
AU - Henzinger, Thomas A
ID - 3855
TI - Qualitative analysis of partially-observable Markov Decision Processes
VL - 6281
ER -
TY - CONF
AB - We consider two-player zero-sum games on graphs. These games can be classified on the basis of the information of the players and on the mode of interaction between them. On the basis of information the classification is as follows: (a) partial-observation (both players have partial view of the game); (b) one-sided complete-observation (one player has complete observation); and (c) complete-observation (both players have complete view of the game). On the basis of mode of interaction we have the following classification: (a) concurrent (players interact simultaneously); and (b) turn-based (players interact in turn). The two sources of randomness in these games are randomness in transition function and randomness in strategies. In general, randomized strategies are more powerful than deterministic strategies, and randomness in transitions gives more general classes of games. We present a complete characterization for the classes of games where randomness is not helpful in: (a) the transition function (probabilistic transition can be simulated by deterministic transition); and (b) strategies (pure strategies are as powerful as randomized strategies). As consequence of our characterization we obtain new undecidability results for these games.
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
AU - Gimbert, Hugo
AU - Henzinger, Thomas A
ID - 3856
TI - Randomness for free
VL - 6281
ER -
TY - CONF
AB - We consider two-player zero-sum games on graphs. On the basis of the information available to the players these games can be classified as follows: (a) partial-observation (both players have partial view of the game); (b) one-sided partial-observation (one player has partial-observation and the other player has complete-observation); and (c) complete-observation (both players have com- plete view of the game). We survey the complexity results for the problem of de- ciding the winner in various classes of partial-observation games with ω-regular winning conditions specified as parity objectives. We present a reduction from the class of parity objectives that depend on sequence of states of the game to the sub-class of parity objectives that only depend on the sequence of observations. We also establish that partial-observation acyclic games are PSPACE-complete.
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
ID - 3858
TI - The complexity of partial-observation parity games
VL - 6397
ER -
TY - CONF
AB - In mean-payoff games, the objective of the protagonist is to ensure that the limit average of an infinite sequence of numeric weights is nonnegative. In energy games, the objective is to ensure that the running sum of weights is always nonnegative. Generalized mean-payoff and energy games replace individual weights by tuples, and the limit average (resp. running sum) of each coordinate must be (resp. remain) nonnegative. These games have applications in the synthesis of resource-bounded processes with multiple resources. We prove the finite-memory determinacy of generalized energy games and show the inter- reducibility of generalized mean-payoff and energy games for finite-memory strategies. We also improve the computational complexity for solving both classes of games with finite-memory strategies: while the previously best known upper bound was EXPSPACE, and no lower bound was known, we give an optimal coNP-complete bound. For memoryless strategies, we show that the problem of deciding the existence of a winning strategy for the protagonist is NP-complete.
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
AU - Henzinger, Thomas A
AU - Raskin, Jean
ID - 3860
TI - Generalized mean-payoff and energy games
VL - 8
ER -
TY - JOUR
AB - We introduce strategy logic, a logic that treats strategies in two-player games as explicit first-order objects. The explicit treatment of strategies allows us to specify properties of nonzero-sum games in a simple and natural way. We show that the one-alternation fragment of strategy logic is strong enough to express the existence of Nash equilibria and secure equilibria, and subsumes other logics that were introduced to reason about games, such as ATL, ATL*, and game logic. We show that strategy logic is decidable, by constructing tree automata that recognize sets of strategies. While for the general logic, our decision procedure is nonelementary, for the simple fragment that is used above we show that the complexity is polynomial in the size of the game graph and optimal in the size of the formula (ranging from polynomial to 2EXPTIME depending on the form of the formula).
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
AU - Piterman, Nir
ID - 3861
IS - 6
JF - Information and Computation
TI - Strategy logic
VL - 208
ER -
TY - JOUR
AB - Quantitative generalizations of classical languages, which assign to each word a real number instead of a Boolean value, have applications in modeling resource-constrained computation. We use weighted automata (finite automata with transition weights) to define several natural classes of quantitative languages over finite and infinite words; in particular, the real value of an infinite run is computed as the maximum, limsup, liminf, limit average, or discounted sum of the transition weights. We define the classical decision problems of automata theory (emptiness, universality, language inclusion, and language equivalence) in the quantitative setting and study their computational complexity. As the decidability of the language-inclusion problem remains open for some classes of weighted automata, we introduce a notion of quantitative simulation that is decidable and implies language inclusion. We also give a complete characterization of the expressive power of the various classes of weighted automata. In particular, we show that most classes of weighted automata cannot be determinized.
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
AU - Henzinger, Thomas A
ID - 3862
IS - 4
JF - ACM Transactions on Computational Logic (TOCL)
TI - Quantitative languages
VL - 11
ER -
TY - JOUR
AB - We consider two-player parity games with imperfect information in which strategies rely on observations that provide imperfect information about the history of a play. To solve such games, i.e., to determine the winning regions of players and corresponding winning strategies, one can use the subset construction to build an equivalent perfect-information game. Recently, an algorithm that avoids the inefficient subset construction has been proposed. The algorithm performs a fixed-point computation in a lattice of antichains, thus maintaining a succinct representation of state sets. However, this representation does not allow to recover winning strategies. In this paper, we build on the antichain approach to develop an algorithm for constructing the winning strategies in parity games of imperfect information. One major obstacle in adapting the classical procedure is that the complementation of attractor sets would break the invariant of downward-closedness on which the antichain representation relies. We overcome this difficulty by decomposing problem instances recursively into games with a combination of reachability, safety, and simpler parity conditions. We also report on an experimental implementation of our algorithm: to our knowledge, this is the first implementation of a procedure for solving imperfect-information parity games on graphs.
AU - Berwanger, Dietmar
AU - Chatterjee, Krishnendu
AU - De Wulf, Martin
AU - Doyen, Laurent
AU - Henzinger, Thomas A
ID - 3863
IS - 10
JF - Information and Computation
TI - Strategy construction for parity games with imperfect information
VL - 208
ER -
TY - CONF
AB - Often one has a preference order among the different systems that satisfy a given specification. Under a probabilistic assumption about the possible inputs, such a preference order is naturally expressed by a weighted automaton, which assigns to each word a value, such that a system is preferred if it generates a higher expected value. We solve the following optimal-synthesis problem: given an omega-regular specification, a Markov chain that describes the distribution of inputs, and a weighted automaton that measures how well a system satisfies the given specification tinder the given input assumption, synthesize a system that optimizes the measured value. For safety specifications and measures that are defined by mean-payoff automata, the optimal-synthesis problem amounts to finding a strategy in a Markov decision process (MDP) that is optimal for a long-run average reward objective, which can be done in polynomial time. For general omega-regular specifications, the solution rests on a new, polynomial-time algorithm for computing optimal strategies in MDPs with mean-payoff parity objectives. We present some experimental results showing optimal systems that were automatically generated in this way.
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
AU - Jobstmann, Barbara
AU - Singh, Rohit
ID - 3864
TI - Measuring and synthesizing systems in probabilistic environments
VL - 6174
ER -
TY - CONF
AB - Systems ought to behave reasonably even in circumstances that are not anticipated in their specifications. We propose a definition of robustness for liveness specifications which prescribes, for any number of environment assumptions that are violated, a minimal number of system guarantees that must still be fulfilled. This notion of robustness can be formulated and realized using a Generalized Reactivity formula. We present an algorithm for synthesizing robust systems from such formulas. For the important special case of Generalized Reactivity formulas of rank 1, our algorithm improves the complexity of [PPS06] for large specifications with a small number of assumptions and guarantees.
AU - Bloem, Roderick
AU - Chatterjee, Krishnendu
AU - Greimel, Karin
AU - Henzinger, Thomas A
AU - Jobstmann, Barbara
ED - Touili, Tayssir
ED - Cook, Byron
ED - Jackson, Paul
ID - 3866
TI - Robustness in the presence of liveness
VL - 6174
ER -
TY - JOUR
AB - Weighted automata are nondeterministic automata with numerical weights on transitions. They can define quantitative languages L that assign to each word w a real number L(w). In the case of infinite words, the value of a run is naturally computed as the maximum, limsup, liminf, limit-average, or discounted-sum of the transition weights. The value of a word w is the supremum of the values of the runs over w. We study expressiveness and closure questions about these quantitative languages. We first show that the set of words with value greater than a threshold can be omega-regular for deterministic limit-average and discounted-sum automata, while this set is always omega-regular when the threshold is isolated (i.e., some neighborhood around the threshold contains no word). In the latter case, we prove that the omega-regular language is robust against small perturbations of the transition weights. We next consider automata with transition weights 0 or 1 and show that they are as expressive as general weighted automata in the limit-average case, but not in the discounted-sum case. Third, for quantitative languages L-1 and L-2, we consider the operations max(L-1, L-2), min(L-1, L-2), and 1 - L-1, which generalize the boolean operations on languages, as well as the sum L-1 + L-2. We establish the closure properties of all classes of quantitative languages with respect to these four operations.
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
AU - Henzinger, Thomas A
ID - 3867
IS - 3
JF - Logical Methods in Computer Science
TI - Expressiveness and closure properties for quantitative languages
VL - 6
ER -
TY - JOUR
AB - Simulation and bisimulation metrics for stochastic systems provide a quantitative generalization of the classical simulation and bisimulation relations. These metrics capture the similarity of states with respect to quantitative specifications written in the quantitative mu-calculus and related probabilistic logics. We first show that the metrics provide a bound for the difference in long-run average and discounted average behavior across states, indicating that the metrics can be used both in system verification, and in performance evaluation. For turn-based games and MDPs, we provide a polynomial-time algorithm for the computation of the one-step metric distance between states. The algorithm is based on linear programming; it improves on the previous known exponential-time algorithm based on a reduction to the theory of reals. We then present PSPACE algorithms for both the decision problem and the problem of approximating the metric distance between two states, matching the best known algorithms for Markov chains. For the bisimulation kernel of the metric our algorithm works in time O(n(4)) for both turn-based games and MDPs; improving the previously best known O(n(9).log(n)) time algorithm for MDPs. For a concurrent game G, we show that computing the exact distance be tween states is at least as hard as computing the value of concurrent reachability games and the square-root-sum problem in computational geometry. We show that checking whether the metric distance is bounded by a rational r, can be done via a reduction to the theory of real closed fields, involving a formula with three quantifier alternations, yielding O(vertical bar G vertical bar(O(vertical bar G vertical bar 5))) time complexity, improving the previously known reduction, which yielded O(vertical bar G vertical bar(O(vertical bar G vertical bar 7))) time complexity. These algorithms can be iterated to approximate the metrics using binary search
AU - Chatterjee, Krishnendu
AU - De Alfaro, Luca
AU - Majumdar, Ritankar
AU - Raman, Vishwanath
ID - 3868
IS - 3
JF - Logical Methods in Computer Science
TI - Algorithms for game metrics
VL - 6
ER -
TY - JOUR
AB - We are interested in 3-dimensional images given as arrays of voxels with intensity values. Extending these values to acontinuous function, we study the robustness of homology classes in its level and interlevel sets, that is, the amount of perturbationneeded to destroy these classes. The structure of the homology classes and their robustness, over all level and interlevel sets, can bevisualized by a triangular diagram of dots obtained by computing the extended persistence of the function. We give a fast hierarchicalalgorithm using the dual complexes of oct-tree approximations of the function. In addition, we show that for balanced oct-trees, thedual complexes are geometrically realized in $R^3$ and can thus be used to construct level and interlevel sets. We apply these tools tostudy 3-dimensional images of plant root systems.
AU - Bendich, Paul
AU - Edelsbrunner, Herbert
AU - Kerber, Michael
ID - 3901
IS - 6
JF - IEEE Transactions of Visualization and Computer Graphics
TI - Computing robustness and persistence for images
VL - 16
ER -
TY - JOUR
AB - Social organisms are constantly exposed to infectious agents via physical contact with conspecifics. While previous work has shown that disease susceptibility at the individual and group level is influenced by gen- etic diversity within and between group members, it remains poorly understood how group-level resistance to pathogens relates directly to individual physiology, defence behaviour and social interactions. We investigated the effects of high versus low genetic diversity on both the individual and collective disease defences in the ant Cardiocondyla obscurior. We compared the antiseptic behaviours (grooming and hygienic behaviour) of workers from genetically homogeneous and diverse colonies after exposure of their brood to the entomopathogenic fungus Metarhizium anisopliae. While workers from diverse colonies performed intensive allogrooming and quickly removed larvae covered with live fungal spores from the nest, workers from homogeneous colonies only removed sick larvae late after infection. This difference was not caused by a reduced repertoire of antiseptic behaviours or a generally decreased brood care activity in ants from homogeneous colonies. Our data instead suggest that reduced genetic diversity compromises the ability of Cardiocondyla colonies to quickly detect or react to the presence of pathogenic fungal spores before an infection is established, thereby affecting the dynamics of social immunity in the colony.
AU - Ugelvig, Line V
AU - Kronauer, Daniel
AU - Schrempf, Alexandra
AU - Heinze, Jürgen
AU - Cremer, Sylvia
ID - 3904
IS - 1695
JF - Proceedings of the Royal Society of London Series B Biological Sciences
TI - Rapid anti-pathogen response in ant societies relies on high genetic diversity
VL - 277
ER -
TY - JOUR
AB - When lymphocytes follow chemotactic cues, they can adopt different migratory modes depending on the geometry and molecular composition of their extracellular environment. In this issue of The EMBO Journal, Klemke et al (2010) describe a novel Ras-dependent chemokine receptor signalling pathway that leads to activation of cofilin, which in turn amplifies actin turnover. This signalling module is exclusively required for lymphocyte migration in three-dimensional (3D) environments, but not for locomotion on two-dimensional (2D) surfaces.
AU - Michele Weber
AU - Michael Sixt
ID - 3960
IS - 17
JF - EMBO Journal
TI - MEK signalling tunes actin treadmilling for interstitial lymphocyte migration
VL - 29
ER -