TY - GEN
AB - We consider partially observable Markov decision processes (POMDPs), that are a standard framework for robotics applications to model uncertainties present in the real world, with temporal logic specifications. All temporal logic specifications in linear-time temporal logic (LTL) can be expressed as parity objectives. We study the qualitative analysis problem for POMDPs with parity objectives that asks whether there is a controller (policy) to ensure that the objective holds with probability 1 (almost-surely). While the qualitative analysis of POMDPs with parity objectives is undecidable, recent results show that when restricted to finite-memory policies the problem is EXPTIME-complete. While the problem is intractable in theory, we present a practical approach to solve the qualitative analysis problem. We designed several heuristics to deal with the exponential complexity, and have used our implementation on a number of well-known POMDP examples for robotics applications. Our results provide the first practical approach to solve the qualitative analysis of robot motion planning with LTL properties in the presence of uncertainty.
AU - Chatterjee, Krishnendu
AU - Chmelik, Martin
AU - Gupta, Raghav
AU - Kanodia, Ayush
ID - 5424
SN - 2664-1690
TI - Qualitative analysis of POMDPs with temporal logic specifications for robotics applications
ER -
TY - GEN
AB - We consider partially observable Markov decision processes (POMDPs) with a set of target states and every transition is associated with an integer cost. The optimization objective we study asks to minimize the expected total cost till the target set is reached, while ensuring that the target set is reached almost-surely (with probability 1). We show that for integer costs approximating the optimal cost is undecidable. For positive costs, our results are as follows: (i) we establish matching lower and upper bounds for the optimal cost and the bound is double exponential; (ii) we show that the problem of approximating the optimal cost is decidable and present approximation algorithms developing on the existing algorithms for POMDPs with finite-horizon objectives. While the worst-case running time of our algorithm is double exponential, we also present efficient stopping criteria for the algorithm and show experimentally that it performs well in many examples of interest.
AU - Anonymous, 1
AU - Anonymous, 2
AU - Anonymous, 3
AU - Anonymous, 4
ID - 5425
SN - 2664-1690
TI - Optimal cost almost-sure reachability in POMDPs
ER -
TY - GEN
AB - We consider partially observable Markov decision processes (POMDPs), that are a standard framework for robotics applications to model uncertainties present in the real world, with temporal logic specifications. All temporal logic specifications in linear-time temporal logic (LTL) can be expressed as parity objectives. We study the qualitative analysis problem for POMDPs with parity objectives that asks whether there is a controller (policy) to ensure that the objective holds with probability 1 (almost-surely). While the qualitative analysis of POMDPs with parity objectives is undecidable, recent results show that when restricted to finite-memory policies the problem is EXPTIME-complete. While the problem is intractable in theory, we present a practical approach to solve the qualitative analysis problem. We designed several heuristics to deal with the exponential complexity, and have used our implementation on a number of well-known POMDP examples for robotics applications. Our results provide the first practical approach to solve the qualitative analysis of robot motion planning with LTL properties in the presence of uncertainty.
AU - Chatterjee, Krishnendu
AU - Chmelik, Martin
AU - Gupta, Raghav
AU - Kanodia, Ayush
ID - 5426
SN - 2664-1690
TI - Qualitative analysis of POMDPs with temporal logic specifications for robotics applications
ER -
TY - GEN
AB - We consider graphs with n nodes together with their tree-decomposition that has b = O ( n ) bags and width t , on the standard RAM computational model with wordsize W = Θ (log n ) . Our contributions are two-fold: Our first contribution is an algorithm that given a graph and its tree-decomposition as input, computes a binary and balanced tree-decomposition of width at most 4 · t + 3 of the graph in O ( b ) time and space, improving a long-standing (from 1992) bound of O ( n · log n ) time for constant treewidth graphs. Our second contribution is on reachability queries for low treewidth graphs. We build on our tree-balancing algorithm and present a data-structure for graph reachability that requires O ( n · t 2 ) preprocessing time, O ( n · t ) space, and O ( d t/ log n e ) time for pair queries, and O ( n · t · log t/ log n ) time for single-source queries. For constant t our data-structure uses O ( n ) time for preprocessing, O (1) time for pair queries, and O ( n/ log n ) time for single-source queries. This is (asymptotically) optimal and is faster than DFS/BFS when answering more than a constant number of single-source queries.
AU - Chatterjee, Krishnendu
AU - Ibsen-Jensen, Rasmus
AU - Pavlogiannis, Andreas
ID - 5427
SN - 2664-1690
TI - Optimal tree-decomposition balancing and reachability on low treewidth graphs
ER -
TY - GEN
AB - Simulation is an attractive alternative for language inclusion for automata as it is an under-approximation of language inclusion, but usually has much lower complexity. For non-deterministic automata, while language inclusion is PSPACE-complete, simulation can be computed in polynomial time. Simulation has also been extended in two orthogonal directions, namely, (1) fair simulation, for simulation over specified set of infinite runs; and (2) quantitative simulation, for simulation between weighted automata. Again, while fair trace inclusion is PSPACE-complete, fair simulation can be computed in polynomial time. For weighted automata, the (quantitative) language inclusion problem is undecidable for mean-payoff automata and the decidability is open for discounted-sum automata, whereas the (quantitative) simulation reduce to mean-payoff games and discounted-sum games, which admit pseudo-polynomial time algorithms.
In this work, we study (quantitative) simulation for weighted automata with Büchi acceptance conditions, i.e., we generalize fair simulation from non-weighted automata to weighted automata. We show that imposing Büchi acceptance conditions on weighted automata changes many fundamental properties of the simulation games. For example, whereas for mean-payoff and discounted-sum games, the players do not need memory to play optimally; we show in contrast that for simulation games with Büchi acceptance conditions, (i) for mean-payoff objectives, optimal strategies for both players require infinite memory in general, and (ii) for discounted-sum objectives, optimal strategies need not exist for both players. While the simulation games with Büchi acceptance conditions are more complicated (e.g., due to infinite-memory requirements for mean-payoff objectives) as compared to their counterpart without Büchi acceptance conditions, we still present pseudo-polynomial time algorithms to solve simulation games with Büchi acceptance conditions for both weighted mean-payoff and weighted discounted-sum automata.
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
AU - Otop, Jan
AU - Velner, Yaron
ID - 5428
SN - 2664-1690
TI - Quantitative fair simulation games
ER -
TY - CHAP
AB - Mechanically coupled cells can generate forces driving cell and tissue morphogenesis during development. Visualization and measuring of these forces is of major importance to better understand the complexity of the biomechanic processes that shape cells and tissues. Here, we describe how UV laser ablation can be utilized to quantitatively assess mechanical tension in different tissues of the developing zebrafish and in cultures of primary germ layer progenitor cells ex vivo.
AU - Smutny, Michael
AU - Behrndt, Martin
AU - Campinho, Pedro
AU - Ruprecht, Verena
AU - Heisenberg, Carl-Philipp J
ED - Nelson, Celeste
ID - 6178
SN - 1064-3745
T2 - Tissue Morphogenesis
TI - UV laser ablation to measure cell and tissue-generated forces in the zebrafish embryo in vivo and ex vivo
VL - 1189
ER -
TY - JOUR
AB - We prove the universality of the β-ensembles with convex analytic potentials and for any β >
0, i.e. we show that the spacing distributions of log-gases at any inverse temperature β coincide with those of the Gaussian β-ensembles.
AU - Erdös, László
AU - Bourgade, Paul
AU - Yau, Horng
ID - 2699
IS - 6
JF - Duke Mathematical Journal
TI - Universality of general β-ensembles
VL - 163
ER -
TY - JOUR
AB - Multi-dimensional mean-payoff and energy games provide the mathematical foundation for the quantitative study of reactive systems, and play a central role in the emerging quantitative theory of verification and synthesis. In this work, we study the strategy synthesis problem for games with such multi-dimensional objectives along with a parity condition, a canonical way to express ω ω -regular conditions. While in general, the winning strategies in such games may require infinite memory, for synthesis the most relevant problem is the construction of a finite-memory winning strategy (if one exists). Our main contributions are as follows. First, we show a tight exponential bound (matching upper and lower bounds) on the memory required for finite-memory winning strategies in both multi-dimensional mean-payoff and energy games along with parity objectives. This significantly improves the triple exponential upper bound for multi energy games (without parity) that could be derived from results in literature for games on vector addition systems with states. Second, we present an optimal symbolic and incremental algorithm to compute a finite-memory winning strategy (if one exists) in such games. Finally, we give a complete characterization of when finite memory of strategies can be traded off for randomness. In particular, we show that for one-dimension mean-payoff parity games, randomized memoryless strategies are as powerful as their pure finite-memory counterparts.
AU - Chatterjee, Krishnendu
AU - Randour, Mickael
AU - Raskin, Jean
ID - 2716
IS - 3-4
JF - Acta Informatica
TI - Strategy synthesis for multi-dimensional quantitative objectives
VL - 51
ER -
TY - JOUR
AB - A robust combiner for hash functions takes two candidate implementations and constructs a hash function which is secure as long as at least one of the candidates is secure. So far, hash function combiners only aim at preserving a single property such as collision-resistance or pseudorandomness. However, when hash functions are used in protocols like TLS they are often required to provide several properties simultaneously. We therefore put forward the notion of robust multi-property combiners and elaborate on different definitions for such combiners. We then propose a combiner that provably preserves (target) collision-resistance, pseudorandomness, and being a secure message authentication code. This combiner satisfies the strongest notion we propose, which requires that the combined function satisfies every security property which is satisfied by at least one of the underlying hash function. If the underlying hash functions have output length n, the combiner has output length 2 n. This basically matches a known lower bound for black-box combiners for collision-resistance only, thus the other properties can be achieved without penalizing the length of the hash values. We then propose a combiner which also preserves the property of being indifferentiable from a random oracle, slightly increasing the output length to 2 n+ω(log n). Moreover, we show how to augment our constructions in order to make them also robust for the one-wayness property, but in this case require an a priory upper bound on the input length.
AU - Fischlin, Marc
AU - Lehmann, Anja
AU - Pietrzak, Krzysztof Z
ID - 2852
IS - 3
JF - Journal of Cryptology
TI - Robust multi-property combiners for hash functions
VL - 27
ER -
TY - CONF
AB - Persistent homology is a recent grandchild of homology that has found use in
science and engineering as well as in mathematics. This paper surveys the method as well
as the applications, neglecting completeness in favor of highlighting ideas and directions.
AU - Edelsbrunner, Herbert
AU - Morozovy, Dmitriy
ID - 2905
TI - Persistent homology: Theory and practice
ER -
TY - BOOK
AB - This monograph presents a short course in computational geometry and topology. In the first part the book covers Voronoi diagrams and Delaunay triangulations, then it presents the theory of alpha complexes which play a crucial role in biology. The central part of the book is the homology theory and their computation, including the theory of persistence which is indispensable for applications, e.g. shape reconstruction. The target audience comprises researchers and practitioners in mathematics, biology, neuroscience and computer science, but the book may also be beneficial to graduate students of these fields.
AU - Edelsbrunner, Herbert
ID - 6853
SN - 2191-530X
TI - A Short Course in Computational Geometry and Topology
ER -
TY - GEN
AU - Huszár, Kristóf
AU - Rolinek, Michal
ID - 7038
TI - Playful Math - An introduction to mathematical games
ER -
TY - JOUR
AB - We propose a method for propagating edit operations in 2D vector graphics, based on geometric relationship functions. These functions quantify the geometric relationship of a point to a polygon, such as the distance to the boundary or the direction to the closest corner vertex. The level sets of the relationship functions describe points with the same relationship to a polygon. For a given query point, we first determine a set of relationships to local features, construct all level sets for these relationships, and accumulate them. The maxima of the resulting distribution are points with similar geometric relationships. We show extensions to handle mirror symmetries, and discuss the use of relationship functions as local coordinate systems. Our method can be applied, for example, to interactive floorplan editing, and it is especially useful for large layouts, where individual edits would be cumbersome. We demonstrate populating 2D layouts with tens to hundreds of objects by propagating relatively few edit operations.
AU - Guerrero, Paul
AU - Jeschke, Stefan
AU - Wimmer, Michael
AU - Wonka, Peter
ID - 1629
IS - 2
JF - ACM Transactions on Graphics
TI - Edit propagation using geometric relationship functions
VL - 33
ER -
TY - CONF
AB - We extend the notion of verifiable random functions (VRF) to constrained VRFs, which generalize the concept of constrained pseudorandom functions, put forward by Boneh and Waters (Asiacrypt’13), and independently by Kiayias et al. (CCS’13) and Boyle et al. (PKC’14), who call them delegatable PRFs and functional PRFs, respectively. In a standard VRF the secret key sk allows one to evaluate a pseudorandom function at any point of its domain; in addition, it enables computation of a non-interactive proof that the function value was computed correctly. In a constrained VRF from the key sk one can derive constrained keys skS for subsets S of the domain, which allow computation of function values and proofs only at points in S. After formally defining constrained VRFs, we derive instantiations from the multilinear-maps-based constrained PRFs by Boneh and Waters, yielding a VRF with constrained keys for any set that can be decided by a polynomial-size circuit. Our VRFs have the same function values as the Boneh-Waters PRFs and are proved secure under the same hardness assumption, showing that verifiability comes at no cost. Constrained (functional) VRFs were stated as an open problem by Boyle et al.
AU - Fuchsbauer, Georg
ED - Abdalla, Michel
ED - De Prisco, Roberto
ID - 1643
T2 - SCN 2014
TI - Constrained Verifiable Random Functions
VL - 8642
ER -
TY - CONF
AB - In this paper we present INTERHORN, a solver for recursion-free Horn clauses. The main application domain of INTERHORN lies in solving interpolation problems arising in software verification. We show how a range of interpolation problems, including path, transition, nested, state/transition and well-founded interpolation can be handled directly by INTERHORN. By detailing these interpolation problems and their Horn clause representations, we hope to encourage the emergence of a common back-end interpolation interface useful for diverse verification tools.
AU - Gupta, Ashutosh
AU - Popeea, Corneliu
AU - Rybalchenko, Andrey
ID - 1702
T2 - Electronic Proceedings in Theoretical Computer Science, EPTCS
TI - Generalised interpolation by solving recursion free-horn clauses
VL - 169
ER -
TY - CONF
AB - It has been long argued that, because of inherent ambiguity and noise, the brain needs to represent uncertainty in the form of probability distributions. The neural encoding of such distributions remains however highly controversial. Here we present a novel circuit model for representing multidimensional real-valued distributions using a spike based spatio-temporal code. Our model combines the computational advantages of the currently competing models for probabilistic codes and exhibits realistic neural responses along a variety of classic measures. Furthermore, the model highlights the challenges associated with interpreting neural activity in relation to behavioral uncertainty and points to alternative population-level approaches for the experimental validation of distributed representations.
AU - Savin, Cristina
AU - Denève, Sophie
ID - 1708
IS - January
TI - Spatio-temporal representations of uncertainty in spiking neural networks
VL - 3
ER -
TY - JOUR
AB - The classical (boolean) notion of refinement for behavioral interfaces of system components is the alternating refinement preorder. In this paper, we define a distance for interfaces, called interface simulation distance. It makes the alternating refinement preorder quantitative by, intuitively, tolerating errors (while counting them) in the alternating simulation game. We show that the interface simulation distance satisfies the triangle inequality, that the distance between two interfaces does not increase under parallel composition with a third interface, that the distance between two interfaces can be bounded from above and below by distances between abstractions of the two interfaces, and how to synthesize an interface from incompatible requirements. We illustrate the framework, and the properties of the distances under composition of interfaces, with two case studies.
AU - Cerny, Pavol
AU - Chmelik, Martin
AU - Henzinger, Thomas A
AU - Radhakrishna, Arjun
ID - 1733
IS - 3
JF - Theoretical Computer Science
TI - Interface simulation distances
VL - 560
ER -
TY - CHAP
AB - The generation of asymmetry, at both cellular and tissue level, is one of the most essential capabilities of all eukaryotic organisms. It mediates basically all multicellular development ranging from embryogenesis and de novo organ formation till responses to various environmental stimuli. In plants, the awe-inspiring number of such processes is regulated by phytohormone auxin and its directional, cell-to-cell transport. The mediators of this transport, PIN auxin transporters, are asymmetrically localized at the plasma membrane, and this polar localization determines the directionality of intercellular auxin flow. Thus, auxin transport contributes crucially to the generation of local auxin gradients or maxima, which instruct given cell to change its developmental program. Here, we introduce and discuss the molecular components and cellular mechanisms regulating the generation and maintenance of cellular PIN polarity, as the general hallmarks of cell polarity in plants.
AU - Baster, Pawel
AU - Friml, Jiří
ED - Zažímalová, Eva
ED - Petrášek, Jan
ED - Benková, Eva
ID - 1806
T2 - Auxin and Its Role in Plant Development
TI - Auxin on the road navigated by cellular PIN polarity
ER -
TY - JOUR
AB - Watermarking techniques for vector graphics dislocate vertices in order to embed imperceptible, yet detectable, statistical features into the input data. The embedding process may result in a change of the topology of the input data, e.g., by introducing self-intersections, which is undesirable or even disastrous for many applications. In this paper we present a watermarking framework for two-dimensional vector graphics that employs conventional watermarking techniques but still provides the guarantee that the topology of the input data is preserved. The geometric part of this framework computes so-called maximum perturbation regions (MPR) of vertices. We propose two efficient algorithms to compute MPRs based on Voronoi diagrams and constrained triangulations. Furthermore, we present two algorithms to conditionally correct the watermarked data in order to increase the watermark embedding capacity and still guarantee topological correctness. While we focus on the watermarking of input formed by straight-line segments, one of our approaches can also be extended to circular arcs. We conclude the paper by demonstrating and analyzing the applicability of our framework in conjunction with two well-known watermarking techniques.
AU - Huber, Stefan
AU - Held, Martin
AU - Meerwald, Peter
AU - Kwitt, Roland
ID - 1816
IS - 1
JF - International Journal of Computational Geometry and Applications
TI - Topology-preserving watermarking of vector graphics
VL - 24
ER -
TY - JOUR
AB - We review recent progress towards a rigorous understanding of the Bogoliubov approximation for bosonic quantum many-body systems. We focus, in particular, on the excitation spectrum of a Bose gas in the mean-field (Hartree) limit. A list of open problems will be discussed at the end.
AU - Seiringer, Robert
ID - 1821
IS - 7
JF - Journal of Mathematical Physics
TI - Bose gases, Bose-Einstein condensation, and the Bogoliubov approximation
VL - 55
ER -