@article{2035,
abstract = {Considering a continuous self-map and the induced endomorphism on homology, we study the eigenvalues and eigenspaces of the latter. Taking a filtration of representations, we define the persistence of the eigenspaces, effectively introducing a hierarchical organization of the map. The algorithm that computes this information for a finite sample is proved to be stable, and to give the correct answer for a sufficiently dense sample. Results computed with an implementation of the algorithm provide evidence of its practical utility.
},
author = {Edelsbrunner, Herbert and Jablonski, Grzegorz and Mrozek, Marian},
journal = {Foundations of Computational Mathematics},
number = {5},
pages = {1213 -- 1244},
publisher = {Springer},
title = {{The persistent homology of a self-map}},
doi = {10.1007/s10208-014-9223-y},
volume = {15},
year = {2015},
}
@article{2085,
abstract = {We study the spectrum of a large system of N identical bosons interacting via a two-body potential with strength 1/N. In this mean-field regime, Bogoliubov's theory predicts that the spectrum of the N-particle Hamiltonian can be approximated by that of an effective quadratic Hamiltonian acting on Fock space, which describes the fluctuations around a condensed state. Recently, Bogoliubov's theory has been justified rigorously in the case that the low-energy eigenvectors of the N-particle Hamiltonian display complete condensation in the unique minimizer of the corresponding Hartree functional. In this paper, we shall justify Bogoliubov's theory for the high-energy part of the spectrum of the N-particle Hamiltonian corresponding to (non-linear) excited states of the Hartree functional. Moreover, we shall extend the existing results on the excitation spectrum to the case of non-uniqueness and/or degeneracy of the Hartree minimizer. In particular, the latter covers the case of rotating Bose gases, when the rotation speed is large enough to break the symmetry and to produce multiple quantized vortices in the Hartree minimizer. },
author = {Nam, Phan and Seiringer, Robert},
journal = {Archive for Rational Mechanics and Analysis},
number = {2},
pages = {381 -- 417},
publisher = {Springer},
title = {{Collective excitations of Bose gases in the mean-field regime}},
doi = {10.1007/s00205-014-0781-6},
volume = {215},
year = {2015},
}
@article{2166,
abstract = {We consider the spectral statistics of large random band matrices on mesoscopic energy scales. We show that the correlation function of the local eigenvalue density exhibits a universal power law behaviour that differs from the Wigner-Dyson- Mehta statistics. This law had been predicted in the physics literature by Altshuler and Shklovskii in (Zh Eksp Teor Fiz (Sov Phys JETP) 91(64):220(127), 1986); it describes the correlations of the eigenvalue density in general metallic sampleswith weak disorder. Our result rigorously establishes the Altshuler-Shklovskii formulas for band matrices. In two dimensions, where the leading term vanishes owing to an algebraic cancellation, we identify the first non-vanishing term and show that it differs substantially from the prediction of Kravtsov and Lerner in (Phys Rev Lett 74:2563-2566, 1995). The proof is given in the current paper and its companion (Ann. H. Poincaré. arXiv:1309.5107, 2014). },
author = {Erdös, László and Knowles, Antti},
journal = {Communications in Mathematical Physics},
number = {3},
pages = {1365 -- 1416},
publisher = {Springer},
title = {{The Altshuler-Shklovskii formulas for random band matrices I: the unimodular case}},
doi = {10.1007/s00220-014-2119-5},
volume = {333},
year = {2015},
}
@article{473,
abstract = {We prove that nonlinear Gibbs measures can be obtained from the corresponding many-body, grand-canonical, quantum Gibbs states, in a mean-field limit where the temperature T diverges and the interaction strength behaves as 1/T. We proceed by characterizing the interacting Gibbs state as minimizing a functional counting the free-energy relatively to the non-interacting case. We then perform an infinite-dimensional analogue of phase-space semiclassical analysis, using fine properties of the quantum relative entropy, the link between quantum de Finetti measures and upper/lower symbols in a coherent state basis, as well as Berezin-Lieb type inequalities. Our results cover the measure built on the defocusing nonlinear Schrödinger functional on a finite interval, as well as smoother interactions in dimensions d 2.},
author = {Lewin, Mathieu and Phan Thanh, Nam and Rougerie, Nicolas},
journal = {Journal de l'Ecole Polytechnique - Mathematiques},
pages = {65 -- 115},
publisher = {Ecole Polytechnique},
title = {{Derivation of nonlinear gibbs measures from many-body quantum mechanics}},
doi = {10.5802/jep.18},
volume = {2},
year = {2015},
}
@article{477,
abstract = {Dendritic cells are potent antigen-presenting cells endowed with the unique ability to initiate adaptive immune responses upon inflammation. Inflammatory processes are often associated with an increased production of serotonin, which operates by activating specific receptors. However, the functional role of serotonin receptors in regulation of dendritic cell functions is poorly understood. Here, we demonstrate that expression of serotonin receptor 5-HT7 (5-HT7TR) as well as its downstream effector Cdc42 is upregulated in dendritic cells upon maturation. Although dendritic cell maturation was independent of 5-HT7TR, receptor stimulation affected dendritic cell morphology through Cdc42-mediated signaling. In addition, basal activity of 5-HT7TR was required for the proper expression of the chemokine receptor CCR7, which is a key factor that controls dendritic cell migration. Consistent with this, we observed that 5-HT7TR enhances chemotactic motility of dendritic cells in vitro by modulating their directionality and migration velocity. Accordingly, migration of dendritic cells in murine colon explants was abolished after pharmacological receptor inhibition. Our results indicate that there is a crucial role for 5-HT7TR-Cdc42-mediated signaling in the regulation of dendritic cell morphology and motility, suggesting that 5-HT7TR could be a new target for treatment of a variety of inflammatory and immune disorders.},
author = {Holst, Katrin and Guseva, Daria and Schindler, Susann and Sixt, Michael K and Braun, Armin and Chopra, Himpriya and Pabst, Oliver and Ponimaskin, Evgeni},
journal = {Journal of Cell Science},
number = {15},
pages = {2866 -- 2880},
publisher = {Company of Biologists},
title = {{The serotonin receptor 5-HT7R regulates the morphology and migratory properties of dendritic cells}},
doi = {10.1242/jcs.167999},
volume = {128},
year = {2015},
}
@article{523,
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},
journal = {Information and Computation},
number = {6},
pages = {25 -- 52},
publisher = {Elsevier},
title = {{Looking at mean-payoff and total-payoff through windows}},
doi = {10.1016/j.ic.2015.03.010},
volume = {242},
year = {2015},
}
@article{524,
abstract = {We consider concurrent games played by two players on a finite-state graph, where in every round the players simultaneously choose a move, and the current state along with the joint moves determine the successor state. We study the most fundamental objective for concurrent games, namely, mean-payoff or limit-average objective, where a reward is associated to each transition, and the goal of player 1 is to maximize the long-run average of the rewards, and the objective of player 2 is strictly the opposite (i.e., the games are zero-sum). The path constraint for player 1 could be qualitative, i.e., the mean-payoff is the maximal reward, or arbitrarily close to it; or quantitative, i.e., a given threshold between the minimal and maximal reward. We consider the computation of the almost-sure (resp. positive) winning sets, where player 1 can ensure that the path constraint is satisfied with probability 1 (resp. positive probability). Almost-sure winning with qualitative constraint exactly corresponds to the question of whether there exists a strategy to ensure that the payoff is the maximal reward of the game. Our main results for qualitative path constraints are as follows: (1) we establish qualitative determinacy results that show that for every state either player 1 has a strategy to ensure almost-sure (resp. positive) winning against all player-2 strategies, or player 2 has a spoiling strategy to falsify almost-sure (resp. positive) winning against all player-1 strategies; (2) we present optimal strategy complexity results that precisely characterize the classes of strategies required for almost-sure and positive winning for both players; and (3) we present quadratic time algorithms to compute the almost-sure and the positive winning sets, matching the best known bound of the algorithms for much simpler problems (such as reachability objectives). For quantitative constraints we show that a polynomial time solution for the almost-sure or the positive winning set would imply a solution to a long-standing open problem (of solving the value problem of turn-based deterministic mean-payoff games) that is not known to be solvable in polynomial time.},
author = {Chatterjee, Krishnendu and Ibsen-Jensen, Rasmus},
journal = {Information and Computation},
number = {6},
pages = {2 -- 24},
publisher = {Elsevier},
title = {{Qualitative analysis of concurrent mean payoff games}},
doi = {10.1016/j.ic.2015.03.009},
volume = {242},
year = {2015},
}
@article{532,
abstract = {Ethylene is a gaseous phytohormone that plays vital roles in plant growth and development. Previous studies uncovered EIN2 as an essential signal transducer linking ethylene perception on ER to transcriptional regulation in the nucleus through a “cleave and shuttle” model. In this study, we report another mechanism of EIN2-mediated ethylene signaling, whereby EIN2 imposes the translational repression of EBF1 and EBF2 mRNA. We find that the EBF1/2 3′ UTRs mediate EIN2-directed translational repression and identify multiple poly-uridylates (PolyU) motifs as functional cis elements of 3′ UTRs. Furthermore, we demonstrate that ethylene induces EIN2 to associate with 3′ UTRs and target EBF1/2 mRNA to cytoplasmic processing-body (P-body) through interacting with multiple P-body factors, including EIN5 and PABs. Our study illustrates translational regulation as a key step in ethylene signaling and presents mRNA 3′ UTR functioning as a “signal transducer” to sense and relay cellular signaling in plants.},
author = {Li, Wenyang and Ma, Mengdi and Feng, Ying and Li, Hongjiang and Wang, Yichuan and Ma, Yutong and Li, Mingzhe and An, Fengying and Guo, Hongwei},
journal = {Cell},
number = {3},
pages = {670 -- 683},
publisher = {Cell Press},
title = {{EIN2-directed translational regulation of ethylene signaling in arabidopsis}},
doi = {10.1016/j.cell.2015.09.037},
volume = {163},
year = {2015},
}
@misc{5429,
abstract = {We consider Markov decision processes (MDPs) with multiple limit-average (or mean-payoff) objectives.
There have been two different views: (i) the expectation semantics, where the goal is to optimize the expected mean-payoff objective, and (ii) the satisfaction semantics, where the goal is to maximize the probability of runs such that the mean-payoff value stays above a given vector.
We consider the problem where the goal is to optimize the expectation under the constraint that the satisfaction semantics is ensured, and thus consider a generalization that unifies the existing semantics.
Our problem captures the notion of optimization with respect to strategies that are risk-averse (i.e., ensures certain probabilistic guarantee).
Our main results are algorithms for the decision problem which are always polynomial in the size of the MDP. We also show that an approximation of the Pareto-curve can be computed in time polynomial in the size of the MDP, and the approximation factor, but exponential in the number of dimensions.
Finally, we present a complete characterization of the strategy complexity (in terms of memory bounds and randomization) required to solve our problem.},
author = {Chatterjee, Krishnendu and Komarkova, Zuzana and Kretinsky, Jan},
issn = {2664-1690},
pages = {41},
publisher = {IST Austria},
title = {{Unifying two views on multiple mean-payoff objectives in Markov decision processes}},
doi = {10.15479/AT:IST-2015-318-v1-1},
year = {2015},
}
@misc{5430,
abstract = {We consider the core algorithmic problems related to verification of systems with respect to three classical quantitative properties, namely, the mean- payoff property, the ratio property, and the minimum initial credit for energy property. The algorithmic problem given a graph and a quantitative property asks to compute the optimal value (the infimum value over all traces) from every node of the graph. We consider graphs with constant treewidth, and it is well-known that the control-flow graphs of most programs have constant treewidth. Let n denote the number of nodes of a graph, m the number of edges (for constant treewidth graphs m = O ( n ) ) and W the largest absolute value of the weights. Our main theoretical results are as follows. First, for constant treewidth graphs we present an algorithm that approximates the mean-payoff value within a mul- tiplicative factor of ∊ in time O ( n · log( n/∊ )) and linear space, as compared to the classical algorithms that require quadratic time. Second, for the ratio property we present an algorithm that for constant treewidth graphs works in time O ( n · log( | a · b · n | )) = O ( n · log( n · W )) , when the output is a b , as compared to the previously best known algorithm with running time O ( n 2 · log( n · W )) . Third, for the minimum initial credit problem we show that (i) for general graphs the problem can be solved in O ( n 2 · m ) time and the associated decision problem can be solved in O ( n · m ) time, improving the previous known O ( n 3 · m · log( n · W )) and O ( n 2 · m ) bounds, respectively; and (ii) for constant treewidth graphs we present an algorithm that requires O ( n · log n ) time, improving the previous known O ( n 4 · log( n · W )) bound. We have implemented some of our algorithms and show that they present a significant speedup on standard benchmarks.},
author = {Chatterjee, Krishnendu and Ibsen-Jensen, Rasmus and Pavlogiannis, Andreas},
issn = {2664-1690},
pages = {31},
publisher = {IST Austria},
title = {{Faster algorithms for quantitative verification in constant treewidth graphs}},
doi = {10.15479/AT:IST-2015-319-v1-1},
year = {2015},
}
@misc{5431,
abstract = {We consider finite-state concurrent stochastic games, played by k>=2 players for an infinite number of rounds, where in every round, each player simultaneously and independently of the other players chooses an action, whereafter the successor state is determined by a probability distribution given by the current state and the chosen actions. We consider reachability objectives that given a target set of states require that some state in the target set is visited, and the dual safety objectives that given a target set require that only states in the target set are visited. We are interested in the complexity of stationary strategies measured by their patience, which is defined as the inverse of the smallest non-zero probability employed.
Our main results are as follows: We show that in two-player zero-sum concurrent stochastic games (with reachability objective for one player and the complementary safety objective for the other player): (i) the optimal bound on the patience of optimal and epsilon-optimal strategies, for both players is doubly exponential; and (ii) even in games with a single non-absorbing state exponential (in the number of actions) patience is necessary. In general we study the class of non-zero-sum games admitting epsilon-Nash equilibria. We show that if there is at least one player with reachability objective, then doubly-exponential patience is needed in general for epsilon-Nash equilibrium strategies, whereas in contrast if all players have safety objectives, then the optimal bound on patience for epsilon-Nash equilibrium strategies is only exponential.},
author = {Chatterjee, Krishnendu and Ibsen-Jensen, Rasmus and Hansen, Kristoffer},
issn = {2664-1690},
pages = {25},
publisher = {IST Austria},
title = {{The patience of concurrent stochastic games with safety and reachability objectives}},
doi = {10.15479/AT:IST-2015-322-v1-1},
year = {2015},
}
@misc{5432,
abstract = {Evolution occurs in populations of reproducing individuals. The structure of the population affects the outcome of the evolutionary process. Evolutionary graph theory is a powerful approach to study this phenomenon. There are two graphs. The interaction graph specifies who interacts with whom in the context of evolution.The replacement graph specifies who competes with whom for reproduction.
The vertices of the two graphs are the same, and each vertex corresponds to an individual of the population. A key quantity is the fixation probability of a new mutant. It is defined as the probability that a newly introduced mutant (on a single vertex) generates a lineage of offspring which eventually takes over the entire population of resident individuals. The basic computational questions are as follows: (i) the qualitative question asks whether the fixation probability is positive; and (ii) the quantitative approximation question asks for an approximation of the fixation probability.
Our main results are:
(1) We show that the qualitative question is NP-complete and the quantitative approximation question is #P-hard in the special case when the interaction and the replacement graphs coincide and even with the restriction that the resident individuals do not reproduce (which corresponds to an invading population taking over an empty structure).
(2) We show that in general the qualitative question is PSPACE-complete and the quantitative approximation question is PSPACE-hard and can be solved in exponential time.
},
author = {Chatterjee, Krishnendu and Ibsen-Jensen, Rasmus and Nowak, Martin},
issn = {2664-1690},
pages = {29},
publisher = {IST Austria},
title = {{The complexity of evolutionary games on graphs}},
doi = {10.15479/AT:IST-2015-323-v1-1},
year = {2015},
}
@misc{5435,
abstract = {We consider Markov decision processes (MDPs) with multiple limit-average (or mean-payoff) objectives.
There have been two different views: (i) the expectation semantics, where the goal is to optimize the expected mean-payoff objective, and (ii) the satisfaction semantics, where the goal is to maximize the probability of runs such that the mean-payoff value stays above a given vector.
We consider the problem where the goal is to optimize the expectation under the constraint that the satisfaction semantics is ensured, and thus consider a generalization that unifies the existing semantics. Our problem captures the notion of optimization with respect to strategies that are risk-averse (i.e., ensures certain probabilistic guarantee).
Our main results are algorithms for the decision problem which are always polynomial in the size of the MDP.
We also show that an approximation of the Pareto-curve can be computed in time polynomial in the size of the MDP, and the approximation factor, but exponential in the number of dimensions. Finally, we present a complete characterization of the strategy complexity (in terms of memory bounds and randomization) required to solve our problem.},
author = {Chatterjee, Krishnendu and Komarkova, Zuzana and Kretinsky, Jan},
issn = {2664-1690},
pages = {51},
publisher = {IST Austria},
title = {{Unifying two views on multiple mean-payoff objectives in Markov decision processes}},
doi = {10.15479/AT:IST-2015-318-v2-1},
year = {2015},
}
@misc{5436,
abstract = {Recently there has been a significant effort to handle quantitative properties in formal verification and synthesis. While weighted automata over finite and infinite words provide a natural and flexible framework to express quantitative properties, perhaps surprisingly, some basic system properties such as average response time cannot be expressed using weighted automata, nor in any other know decidable formalism. In this work, we introduce nested weighted automata as a natural extension of weighted automata which makes it possible to express important quantitative properties such as average response time.
In nested weighted automata, a master automaton spins off and collects results from weighted slave automata, each of which computes a quantity along a finite portion of an infinite word. Nested weighted automata can be viewed as the quantitative analogue of monitor automata, which are used in run-time verification. We establish an almost complete decidability picture for the basic decision problems about nested weighted automata, and illustrate their applicability in several domains. In particular, nested weighted automata can be used to decide average response time properties.},
author = {Chatterjee, Krishnendu and Henzinger, Thomas A and Otop, Jan},
issn = {2664-1690},
pages = {29},
publisher = {IST Austria},
title = {{Nested weighted automata}},
doi = {10.15479/AT:IST-2015-170-v2-2},
year = {2015},
}
@misc{5437,
abstract = {We consider the core algorithmic problems related to verification of systems with respect to three classical quantitative properties, namely, the mean-payoff property, the ratio property, and the minimum initial credit for energy property.
The algorithmic problem given a graph and a quantitative property asks to compute the optimal value (the infimum value over all traces) from every node of the graph. We consider graphs with constant treewidth, and it is well-known that the control-flow graphs of most programs have constant treewidth. Let $n$ denote the number of nodes of a graph, $m$ the number of edges (for constant treewidth graphs $m=O(n)$) and $W$ the largest absolute value of the weights.
Our main theoretical results are as follows.
First, for constant treewidth graphs we present an algorithm that approximates the mean-payoff value within a multiplicative factor of $\epsilon$ in time $O(n \cdot \log (n/\epsilon))$ and linear space, as compared to the classical algorithms that require quadratic time. Second, for the ratio property we present an algorithm that for constant treewidth graphs works in time $O(n \cdot \log (|a\cdot b|))=O(n\cdot\log (n\cdot W))$, when the output is $\frac{a}{b}$, as compared to the previously best known algorithm with running time $O(n^2 \cdot \log (n\cdot W))$. Third, for the minimum initial credit problem we show that (i)~for general graphs the problem can be solved in $O(n^2\cdot m)$ time and the associated decision problem can be solved in $O(n\cdot m)$ time, improving the previous known $O(n^3\cdot m\cdot \log (n\cdot W))$ and $O(n^2 \cdot m)$ bounds, respectively; and (ii)~for constant treewidth graphs we present an algorithm that requires $O(n\cdot \log n)$ time, improving the previous known $O(n^4 \cdot \log (n \cdot W))$ bound.
We have implemented some of our algorithms and show that they present a significant speedup on standard benchmarks. },
author = {Chatterjee, Krishnendu and Ibsen-Jensen, Rasmus and Pavlogiannis, Andreas},
issn = {2664-1690},
pages = {27},
publisher = {IST Austria},
title = {{Faster algorithms for quantitative verification in constant treewidth graphs}},
doi = {10.15479/AT:IST-2015-330-v2-1},
year = {2015},
}
@misc{5438,
abstract = {The edit distance between two words w1, w2 is the minimal number of word operations (letter insertions, deletions, and substitutions) necessary to transform w1 to w2. The edit distance generalizes to languages L1, L2, where the edit distance is the minimal number k such that for every word from L1 there exists a word in L2 with edit distance at most k. We study the edit distance computation problem between pushdown automata and their subclasses.
The problem of computing edit distance to a pushdown automaton is undecidable, and in practice, the interesting question is to compute the edit distance from a pushdown automaton (the implementation, a standard model for programs with recursion) to a regular language (the specification). In this work, we present a complete picture of decidability and complexity for deciding whether, for a given threshold k, the edit distance from a pushdown automaton to a finite automaton is at most k. },
author = {Chatterjee, Krishnendu and Henzinger, Thomas A and Ibsen-Jensen, Rasmus and Otop, Jan},
issn = {2664-1690},
pages = {15},
publisher = {IST Austria},
title = {{Edit distance for pushdown automata}},
doi = {10.15479/AT:IST-2015-334-v1-1},
year = {2015},
}
@misc{5439,
abstract = {The target discounted-sum problem is the following: Given a rational discount factor 0 < λ < 1 and three rational values a, b, and t, does there exist a finite or an infinite sequence w ε(a, b)∗ or w ε(a, b)w, such that Σ|w| i=0 w(i)λi equals t? The problem turns out to relate to many fields of mathematics and computer science, and its decidability question is surprisingly hard to solve. We solve the finite version of the problem, and show the hardness of the infinite version, linking it to various areas and open problems in mathematics and computer science: β-expansions, discounted-sum automata, piecewise affine maps, and generalizations of the Cantor set. We provide some partial results to the infinite version, among which are solutions to its restriction to eventually-periodic sequences and to the cases that λ λ 1/2 or λ = 1/n, for every n ε N. We use our results for solving some open problems on discounted-sum automata, among which are the exact-value problem for nondeterministic automata over finite words and the universality and inclusion problems for functional automata. },
author = {Boker, Udi and Henzinger, Thomas A and Otop, Jan},
issn = {2664-1690},
pages = {20},
publisher = {IST Austria},
title = {{The target discounted-sum problem}},
doi = {10.15479/AT:IST-2015-335-v1-1},
year = {2015},
}
@misc{5440,
abstract = {Evolution occurs in populations of reproducing individuals. The structure of the population affects the outcome of the evolutionary process. Evolutionary graph theory is a powerful approach to study this phenomenon. There are two graphs. The interaction graph specifies who interacts with whom for payoff in the context of evolution. The replacement graph specifies who competes with whom for reproduction. The vertices of the two graphs are the same, and each vertex corresponds to an individual of the population. The fitness (or the reproductive rate) is a non-negative number, and depends on the payoff. A key quantity is the fixation probability of a new mutant. It is defined as the probability that a newly introduced mutant (on a single vertex) generates a lineage of offspring which eventually takes over the entire population of resident individuals. The basic computational questions are as follows: (i) the qualitative question asks whether the fixation probability is positive; and (ii) the quantitative approximation question asks for an approximation of the fixation probability. Our main results are as follows: First, we consider a special case of the general problem, where the residents do not reproduce. We show that the qualitative question is NP-complete, and the quantitative approximation question is #P-complete, and the hardness results hold even in the special case where the interaction and the replacement graphs coincide. Second, we show that in general both the qualitative and the quantitative approximation questions are PSPACE-complete. The PSPACE-hardness result for quantitative approximation holds even when the fitness is always positive.},
author = {Chatterjee, Krishnendu and Ibsen-Jensen, Rasmus and Nowak, Martin},
issn = {2664-1690},
pages = {18},
publisher = {IST Austria},
title = {{The complexity of evolutionary games on graphs}},
doi = {10.15479/AT:IST-2015-323-v2-2},
year = {2015},
}
@misc{5441,
abstract = {We study algorithmic questions for concurrent systems where the transitions are labeled from a complete, closed semiring, and path properties are algebraic with semiring operations. The algebraic path properties can model dataflow analysis problems, the shortest path problem, and many other natural problems that arise in program analysis. We consider that each component of the concurrent system is a graph with constant treewidth, a property satisfied by the controlflow graphs of most programs. We allow for multiple possible queries, which arise naturally in demand driven dataflow analysis. The study of multiple queries allows us to consider the tradeoff between the resource usage of the one-time preprocessing and for each individual query. The traditional approach constructs the product graph of all components and applies the best-known graph algorithm on the product. In this approach, even the answer to a single query requires the transitive closure (i.e., the results of all possible queries), which provides no room for tradeoff between preprocessing and query time. Our main contributions are algorithms that significantly improve the worst-case running time of the traditional approach, and provide various tradeoffs depending on the number of queries. For example, in a concurrent system of two components, the traditional approach requires hexic time in the worst case for answering one query as well as computing the transitive closure, whereas we show that with one-time preprocessing in almost cubic time, each subsequent query can be answered in at most linear time, and even the transitive closure can be computed in almost quartic time. Furthermore, we establish conditional optimality results showing that the worst-case running time of our algorithms cannot be improved without achieving major breakthroughs in graph algorithms (i.e., improving the worst-case bound for the shortest path problem in general graphs). Preliminary experimental results show that our algorithms perform favorably on several benchmarks.},
author = {Chatterjee, Krishnendu and Ibsen-Jensen, Rasmus and Goharshady, Amir and Pavlogiannis, Andreas},
issn = {2664-1690},
pages = {24},
publisher = {IST Austria},
title = {{Algorithms for algebraic path properties in concurrent systems of constant treewidth components}},
doi = {10.15479/AT:IST-2015-340-v1-1},
year = {2015},
}
@misc{5443,
abstract = {POMDPs are standard models for probabilistic planning problems, where an agent interacts with an uncertain environment. We study the problem of almost-sure reachability, where given a set of target states, the question is to decide whether there is a policy to ensure that the target set is reached with probability 1 (almost-surely). While in general the problem is EXPTIME-complete, in many practical cases policies with a small amount of memory suffice. Moreover, the existing solution to the problem is explicit, which first requires to construct explicitly an exponential reduction to a belief-support MDP. In this work, we first study the existence of observation-stationary strategies, which is NP-complete, and then small-memory strategies. We present a symbolic algorithm by an efficient encoding to SAT and using a SAT solver for the problem. We report experimental results demonstrating the scalability of our symbolic (SAT-based) approach.},
author = {Chatterjee, Krishnendu and Chmelik, Martin and Davies, Jessica},
issn = {2664-1690},
pages = {23},
publisher = {IST Austria},
title = {{A symbolic SAT-based algorithm for almost-sure reachability with small strategies in POMDPs}},
doi = {10.15479/AT:IST-2015-325-v2-1},
year = {2015},
}