@inproceedings{18350,
  abstract     = {We introduce an (equi-)affine invariant geometric structure by which surfaces that go through squeeze and shear transformations can still be properly analyzed. The definition of an affine invariant metric enables us to evaluate a new form of geodesic distances and to construct an invariant Laplacian from which local and global diffusion geometry is constructed. Applications of the proposed framework demonstrate its power in generalizing and enriching the existing set of tools for shape analysis.},
  author       = {Raviv, Dan and Bronstein, Alexander and Bronstein, Michael M. and Kimmel, Ron and Sochen, Nir},
  booktitle    = {15th International Workshop on Theoretical Foundations of Computer Vision},
  isbn         = {9783642340901},
  issn         = {1611-3349},
  location     = {Dagstuhl, Germany},
  pages        = {177--190},
  publisher    = {Springer Nature},
  title        = {{Equi-affine invariant geometries of articulated objects}},
  doi          = {10.1007/978-3-642-34091-8_8},
  volume       = {7474},
  year         = {2012},
}

@article{18364,
  abstract     = {Region feature detectors and descriptors have become a successful and popular alternative to point descriptors in image analysis due to their high robustness and repeatability, leading to a significant interest in the shape analysis community in finding analogous approaches in the 3D world. Recent works have successfully extended the maximally stable extremal region (MSER) detection algorithm to surfaces. In many applications, however, a volumetric shape model is more appropriate, and modeling shape deformations as approximate isometries of the volume of an object, rather than its boundary, better captures natural behavior of non-rigid deformations. In this paper, we formulate a diffusion-geometric framework for volumetric stable component detection and description in deformable shapes. An evaluation of our method on the SHREC'11 feature detection benchmark and SCAPE human body scans shows its potential as a source of high-quality features. Examples demonstrating the drawbacks of surface stable components and the advantage of their volumetric counterparts are also presented.},
  author       = {Litman, R. and Bronstein, Alexander and Bronstein, M.M.},
  issn         = {0097-8493},
  journal      = {Computers & Graphics},
  number       = {5},
  pages        = {569--576},
  publisher    = {Elsevier},
  title        = {{Stable volumetric features in deformable shapes}},
  doi          = {10.1016/j.cag.2012.03.034},
  volume       = {36},
  year         = {2012},
}

@inproceedings{18378,
  abstract     = {In this work, we present intrinsic shape context (ISC) descriptors for 3D shapes. We generalize to surfaces the polar sampling of the image domain used in shape contexts: for this purpose, we chart the surface by shooting geodesic outwards from the point being analyzed; `angle' is treated as tantamount to geodesic shooting direction, and radius as geodesic distance. To deal with orientation ambiguity, we exploit properties of the Fourier transform. Our charting method is intrinsic, i.e., invariant to isometric shape transformations. The resulting descriptor is a meta-descriptor that can be applied to any photometric or geometric property field defined on the shape, in particular, we can leverage recent developments in intrinsic shape analysis and construct ISC based on state-of-the-art dense shape descriptors such as heat kernel signatures. Our experiments demonstrate a notable improvement in shape matching on standard benchmarks.},
  author       = {Kokkinos, I. and Bronstein, M. M. and Litman, R. and Bronstein, Alexander},
  booktitle    = {2012 IEEE Conference on Computer Vision and Pattern Recognition},
  isbn         = {9781467312264},
  issn         = {1063-6919},
  location     = {Providence, RI, United States},
  publisher    = {IEEE},
  title        = {{Intrinsic shape context descriptors for deformable shapes}},
  doi          = {10.1109/cvpr.2012.6247671},
  year         = {2012},
}

@inproceedings{18379,
  abstract     = {We consider the problem of minimum distortion intrinsic correspondence between deformable shapes, many useful formulations of which give rise to the NP-hard quadratic assignment problem (QAP). Previous attempts to use the spectral relaxation have had limited success due to the lack of sparsity of the obtained “fuzzy” solution. In this paper, we adopt the recently introduced alternative L 1 relaxation of the QAP based on the principles of game theory. We relate it to the Gromov and Lipschitz metrics between metric spaces and demonstrate on state-of-the-art benchmarks that the proposed approach is capable of finding very accurate sparse correspondences between deformable shapes.},
  author       = {Rodola, E. and Bronstein, Alexander and Albarelli, A. and Bergamasco, F. and Torsello, A.},
  booktitle    = {2012 IEEE Conference on Computer Vision and Pattern Recognition},
  isbn         = {978-1-4673-1226-4},
  issn         = {1063-6919},
  location     = {Providence, RI, United States},
  publisher    = {IEEE},
  title        = {{A game-theoretic approach to deformable shape matching}},
  doi          = {10.1109/cvpr.2012.6247674},
  year         = {2012},
}

@article{18412,
  abstract     = {SIFT-like local feature descriptors are ubiquitously employed in computer vision applications such as content-based retrieval, video analysis, copy detection, object recognition, photo tourism, and 3D reconstruction. Feature descriptors can be designed to be invariant to certain classes of photometric and geometric transformations, in particular, affine and intensity scale transformations. However, real transformations that an image can undergo can only be approximately modeled in this way, and thus most descriptors are only approximately invariant in practice. Second, descriptors are usually high dimensional (e.g., SIFT is represented as a 128--dimensional vector). In large-scale retrieval and matching problems, this can pose challenges in storing and retrieving descriptor data. We map the descriptor vectors into the Hamming space in which the Hamming metric is used to compare the resulting representations. This way, we reduce the size of the descriptors by representing them as short binary strings and learn descriptor invariance from examples. We show extensive experimental validation, demonstrating the advantage of the proposed approach.},
  author       = {Strecha, C. and Bronstein, Alexander and Bronstein, M. M. and Fua, P.},
  issn         = {2160-9292},
  journal      = {IEEE Transactions on Pattern Analysis and Machine Intelligence},
  number       = {1},
  pages        = {66--78},
  publisher    = {Institute of Electrical and Electronics Engineers},
  title        = {{LDAHash: Improved matching with smaller descriptors}},
  doi          = {10.1109/tpami.2011.103},
  volume       = {34},
  year         = {2012},
}

@article{22056,
  abstract     = {We consider the mass-critical generalized Korteweg{de Vries equation (∂t + ∂xxx)u = ±∂ x(u 5) for real-valued functions u(t; x). We prove that if the global well-posedness and scattering conjecture for this equation failed, then, conditional on a positive answer to the global well-posedness and scattering conjecture for the masscritical nonlinear Schrffodinger equation (-i∂ t + ∂xx)u = ±(|u| 4u), there exists a minimal-mass blowup solution to the mass-critical generalized KdV equation which is almost periodic modulo the symmetries of the equation. Moreover, we can guarantee that this minimal-mass blowup solution is either a self-similar solution, a soliton-like solution, or a double high-to-low frequency cascade solution.},
  author       = {Killip, Rowan and Kwon, Soonsik and Shao, Shuanglin and Visan, Monica},
  issn         = {1553-5231},
  journal      = {Discrete and Continuous Dynamical Systems},
  number       = {1},
  pages        = {191--221},
  publisher    = {American Institute of Mathematical Sciences},
  title        = {{On the mass-critical generalized KdV equation}},
  doi          = {10.3934/dcds.2012.32.191},
  volume       = {32},
  year         = {2012},
}

@article{22075,
  abstract     = {In this short note, we present a new proof of the global well-posedness and scattering result for the defocusing energy-critical nonlinear Schrödinger equation (NLS) in four space dimensions obtained previously by Ryckman and Visan [“Global well-posedness and scattering for the defocusing energycritical nonlinear Schrödinger equation in R^1+4⁠.” American Journal of Mathematics 129 (2007): 1–60. MR2288737]. The argument is inspired by the recent work of Dodson [“Global well-posedness and scattering for the defocusing, L2-critical, nonlinear Schrödinger equation when d≥3.” (2009): preprint arXiv:0912.2467.] on the mass-critical NLS.},
  author       = {Visan, Monica},
  issn         = {1687-0247},
  journal      = {International Mathematics Research Notices},
  number       = {5},
  pages        = {1037--1067},
  publisher    = {Oxford University Press},
  title        = {{Global well-posedness and scattering for the defocusing cubic nonlinear Schrödinger equation in four dimensions}},
  doi          = {10.1093/imrn/rnr051},
  volume       = {2012},
  year         = {2012},
}

@article{2318,
  abstract     = {We show that bosons interacting via pair potentials with negative scattering length form bound states for a suitable number of particles. In other words, the absence of many-particle bound states of any kind implies the non-negativity of the scattering length of the interaction potential. },
  author       = {Seiringer, Robert},
  journal      = {Journal of Spectral Theory},
  number       = {3},
  pages        = {321--328},
  publisher    = {EMS Press},
  title        = {{Absence of bound states implies non-negativity of the scattering length}},
  doi          = {10.4171/JST/31},
  volume       = {2},
  year         = {2012},
}

@article{2954,
  abstract     = {Spontaneous postsynaptic currents (PSCs) provide key information about the mechanisms of synaptic transmission and the activity modes of neuronal networks. However, detecting spontaneous PSCs in vitro and in vivo has been challenging, because of the small amplitude, the variable kinetics, and the undefined time of generation of these events. Here, we describe a, to our knowledge, new method for detecting spontaneous synaptic events by deconvolution, using a template that approximates the average time course of spontaneous PSCs. A recorded PSC trace is deconvolved from the template, resulting in a series of delta-like functions. The maxima of these delta-like events are reliably detected, revealing the precise onset times of the spontaneous PSCs. Among all detection methods, the deconvolution-based method has a unique temporal resolution, allowing the detection of individual events in high-frequency bursts. Furthermore, the deconvolution-based method has a high amplitude resolution, because deconvolution can substantially increase the signal/noise ratio. When tested against previously published methods using experimental data, the deconvolution-based method was superior for spontaneous PSCs recorded in vivo. Using the high-resolution deconvolution-based detection algorithm, we show that the frequency of spontaneous excitatory postsynaptic currents in dentate gyrus granule cells is 4.5 times higher in vivo than in vitro.},
  author       = {Pernia-Andrade, Alejandro and Goswami, Sarit and Stickler, Yvonne and Fröbe, Ulrich and Schlögl, Alois and Jonas, Peter M},
  journal      = {Biophysical Journal},
  number       = {7},
  pages        = {1429 -- 1439},
  publisher    = {Biophysical Society},
  title        = {{A deconvolution based method with high sensitivity and temporal resolution for detection of spontaneous synaptic currents in vitro and in vivo}},
  doi          = {10.1016/j.bpj.2012.08.039},
  volume       = {103},
  year         = {2012},
}

@article{3160,
  abstract     = {There is a long-running controversy about how early cell fate decisions are made in the developing mammalian embryo. 1,2 In particular, it is controversial when the first events that can predict the establishment of the pluripotent and extra-embryonic lineages in the blastocyst of the pre-implantation embryo occur. It has long been proposed that the position and polarity of cells at the 16- to 32-cell stage embryo influence their decision to either give rise to the pluripotent cell lineage that eventually contributes to the inner cell mass (ICM), comprising the primitive endoderm (PE) and the epiblast (EPI), or the extra-embryonic trophectoderm (TE) surrounding the blastocoel. The positioning of cells in the embryo at this developmental stage could largely be the result of random events, making this a stochastic model of cell lineage allocation. Contrary to such a stochastic model, some studies have detected putative differences in the lineage potential of individual blastomeres before compaction, indicating that the first cell fate decisions may occur as early as at the 4-cell stage. Using a non-invasive, quantitative in vivo imaging assay to study the kinetic behavior of Oct4 (also known as POU5F1), a key transcription factor (TF) controlling pre-implantation development in the mouse embryo, 3-5 a recent study identifies Oct4 kinetics as a predictive measure of cell lineage patterning in the early mouse embryo. 6 Here, we discuss the implications of such molecular heterogeneities in early development and offer potential avenues toward a mechanistic understanding of these observations, contributing to the resolution of the controversy of developmental cell lineage allocation.},
  author       = {Pantazis, Periklis and Bollenbach, Tobias},
  journal      = {Cell Cycle},
  number       = {11},
  pages        = {2055 -- 2058},
  publisher    = {Taylor & Francis},
  title        = {{Transcription factor kinetics and the emerging asymmetry in the early mammalian embryo}},
  doi          = {10.4161/cc.20118},
  volume       = {11},
  year         = {2012},
}

@inproceedings{2048,
  abstract     = {Leakage resilient cryptography attempts to incorporate side-channel leakage into the black-box security model and designs cryptographic schemes that are provably secure within it. Informally, a scheme is leakage-resilient if it remains secure even if an adversary learns a bounded amount of arbitrary information about the schemes internal state. Unfortunately, most leakage resilient schemes are unnecessarily complicated in order to achieve strong provable security guarantees. As advocated by Yu et al. [CCS’10], this mostly is an artefact of the security proof and in practice much simpler construction may already suffice to protect against realistic side-channel attacks. In this paper, we show that indeed for simpler constructions leakage-resilience can be obtained when we aim for relaxed security notions where the leakage-functions and/or the inputs to the primitive are chosen non-adaptively. For example, we show that a three round Feistel network instantiated with a leakage resilient PRF yields a leakage resilient PRP if the inputs are chosen non-adaptively (This complements the result of Dodis and Pietrzak [CRYPTO’10] who show that if a adaptive queries are allowed, a superlogarithmic number of rounds is necessary.) We also show that a minor variation of the classical GGM construction gives a leakage resilient PRF if both, the leakage-function and the inputs, are chosen non-adaptively.},
  author       = {Faust, Sebastian and Pietrzak, Krzysztof Z and Schipper, Joachim},
  booktitle    = {Conference proceedings CHES 2012},
  location     = {Leuven, Belgium},
  pages        = {213 -- 232},
  publisher    = {Springer},
  title        = {{Practical leakage-resilient symmetric cryptography}},
  doi          = {10.1007/978-3-642-33027-8_13},
  volume       = {7428},
  year         = {2012},
}

@inproceedings{2049,
  abstract     = {We propose a new authentication protocol that is provably secure based on a ring variant of the learning parity with noise (LPN) problem. The protocol follows the design principle of the LPN-based protocol from Eurocrypt’11 (Kiltz et al.), and like it, is a two round protocol secure against active attacks. Moreover, our protocol has small communication complexity and a very small footprint which makes it applicable in scenarios that involve low-cost, resource-constrained devices.

Performance-wise, our protocol is more efficient than previous LPN-based schemes, such as the many variants of the Hopper-Blum (HB) protocol and the aforementioned protocol from Eurocrypt’11. Our implementation results show that it is even comparable to the standard challenge-and-response protocols based on the AES block-cipher. Our basic protocol is roughly 20 times slower than AES, but with the advantage of having 10 times smaller code size. Furthermore, if a few hundred bytes of non-volatile memory are available to allow the storage of some off-line pre-computations, then the online phase of our protocols is only twice as slow as AES.
},
  author       = {Heyse, Stefan and Kiltz, Eike and Lyubashevsky, Vadim and Paar, Christof and Pietrzak, Krzysztof Z},
  booktitle    = {Conference proceedings FSE 2012},
  location     = {Washington, DC, USA},
  pages        = {346 -- 365},
  publisher    = {Springer},
  title        = {{Lapin: An efficient authentication protocol based on ring-LPN}},
  doi          = {10.1007/978-3-642-34047-5_20},
  volume       = {7549},
  year         = {2012},
}

@inproceedings{2942,
  abstract     = {Interface theories provide a formal framework for component-based development of software and hardware which supports the incremental design of systems and the independent implementability of components. These capabilities are ensured through mathematical properties of the parallel composition operator and the refinement relation for components. More recently, a conjunction operation was added to interface theories in order to provide support for handling multiple viewpoints, requirements engineering, and component reuse. Unfortunately, the conjunction operator does not allow independent implementability in general. In this paper, we study conditions that need to be imposed on interface models in order to enforce independent implementability with respect to conjunction. We focus on multiple viewpoint specifications and propose a new compatibility criterion between two interfaces, which we call orthogonality. We show that orthogonal interfaces can be refined separately, while preserving both orthogonality and composability with other interfaces. We illustrate the independent implementability of different viewpoints with a FIFO buffer example.},
  author       = {Henzinger, Thomas A and Nickovic, Dejan},
  booktitle    = {Conference proceedings Monterey Workshop 2012},
  location     = {Oxford, UK},
  pages        = {380 -- 395},
  publisher    = {Springer},
  title        = {{Independent implementability of viewpoints}},
  doi          = {10.1007/978-3-642-34059-8_20},
  volume       = {7539},
  year         = {2012},
}

@article{3274,
  abstract     = {A boundary element model of a tunnel running through horizontally layered soil with anisotropic material properties is presented. Since there is no analytical fundamental solution for wave propagation inside a layered orthotropic medium in 3D, the fundamental displacements and stresses have to be calculated numerically. In our model this is done in the Fourier domain with respect to space and time. The assumption of a straight tunnel with infinite extension in the x direction makes it possible to decouple the system for every wave number kx, leading to a 2.5D-problem, which is suited for parallel computation. The special form of the fundamental solution, resulting from our Fourier ansatz, and the fact, that the calculation of the boundary integral equation is performed in the Fourier domain, enhances the stability and efficiency of the numerical calculations.},
  author       = {Rieckh, Georg and Kreuzer, Wolfgang and Waubke, Holger and Balazs, Peter},
  journal      = {Engineering Analysis with Boundary Elements},
  number       = {6},
  pages        = {960 -- 967},
  publisher    = {Elsevier},
  title        = {{A 2.5D-Fourier-BEM model for vibrations in a tunnel running through layered anisotropic soil}},
  doi          = {10.1016/j.enganabound.2011.12.014},
  volume       = {36},
  year         = {2012},
}

@article{3331,
  abstract     = {Computing the topology of an algebraic plane curve C means computing a combinatorial graph that is isotopic to C and thus represents its topology in R2. We prove that, for a polynomial of degree n with integer coefficients bounded by 2ρ, the topology of the induced curve can be computed with  bit operations ( indicates that we omit logarithmic factors). Our analysis improves the previous best known complexity bounds by a factor of n2. The improvement is based on new techniques to compute and refine isolating intervals for the real roots of polynomials, and on the consequent amortized analysis of the critical fibers of the algebraic curve.},
  author       = {Kerber, Michael and Sagraloff, Michael},
  journal      = {Journal of Symbolic Computation},
  number       = {3},
  pages        = {239 -- 258},
  publisher    = {Elsevier},
  title        = {{A worst case bound for topology computation of algebraic curves}},
  doi          = {10.1016/j.jsc.2011.11.001},
  volume       = {47},
  year         = {2012},
}

@inproceedings{2955,
  abstract     = {We consider two-player stochastic games played on finite graphs with reachability objectives where the first player tries to ensure a target state to be visited almost-surely (i.e., with probability 1), or positively (i.e., with positive probability), no matter the strategy of the second player. We classify such games according to the information and the power of randomization available to the players. On the basis of information, the game can be one-sided with either (a) player 1, or (b) player 2 having partial observation (and the other player has perfect observation), or two-sided with (c) both players having partial observation. On the basis of randomization, the players (a) may not be allowed to use randomization (pure strategies), or (b) may choose a probability distribution over actions but the actual random choice is external and not visible to the player (actions invisible), or (c) may use full randomization. Our main results for pure strategies are as follows. (1) For one-sided games with player 1 having partial observation we show that (in contrast to full randomized strategies) belief-based (subset-construction based) strategies are not sufficient, and we present an exponential upper bound on memory both for almostsure and positive winning strategies; we show that the problem of deciding the existence of almost-sure and positive winning strategies for player 1 is EXPTIME-complete. (2) For one-sided games with player 2 having partial observation we show that non-elementary memory is both necessary and sufficient for both almost-sure and positive winning strategies. (3) We show that for the general (two-sided) case finite-memory strategies are sufficient for both positive and almost-sure winning, and at least non-elementary memory is required. We establish the equivalence of the almost-sure winning problems for pure strategies and for randomized strategies with actions invisible. Our equivalence result exhibits serious flaws in previous results of the literature: we show a non-elementary memory lower bound for almost-sure winning whereas an exponential upper bound was previously claimed.},
  author       = {Chatterjee, Krishnendu and Doyen, Laurent},
  booktitle    = {Proceedings of the 2012 27th Annual ACM/IEEE Symposium on Logic in Computer Science},
  location     = {Dubrovnik, Croatia},
  publisher    = {IEEE},
  title        = {{Partial-observation stochastic games: How to win when belief fails}},
  doi          = {10.1109/LICS.2012.28},
  year         = {2012},
}

@article{2967,
  abstract     = {For programs whose data variables range over Boolean or finite domains, program verification is decidable, and this forms the basis of recent tools for software model checking. In this article, we consider algorithmic verification of programs that use Boolean variables, and in addition, access a single read-only array whose length is potentially unbounded, and whose elements range over an unbounded data domain. We show that the reachability problem, while undecidable in general, is (1) PSPACE-complete for programs in which the array-accessing for-loops are not nested, (2) decidable for a restricted class of programs with doubly nested loops. The second result establishes connections to automata and logics defining languages over data words.},
  author       = {Alur, Rajeev and Cerny, Pavol and Weinstein, Scott},
  journal      = {ACM Transactions on Computational Logic},
  number       = {3},
  publisher    = {ACM},
  title        = {{Algorithmic analysis of array-accessing programs}},
  doi          = {10.1145/2287718.2287727},
  volume       = {13},
  year         = {2012},
}

@article{494,
  abstract     = {We solve the longstanding open problems of the blow-up involved in the translations, when possible, of a nondeterministic Büchi word automaton (NBW) to a nondeterministic co-Büchi word automaton (NCW) and to a deterministic co-Büchi word automaton (DCW). For the NBW to NCW translation, the currently known upper bound is 2o(nlog n) and the lower bound is 1.5n. We improve the upper bound to n2n and describe a matching lower bound of 2ω(n). For the NBW to DCW translation, the currently known upper bound is 2o(nlog n). We improve it to 2 o(n), which is asymptotically tight. Both of our upper-bound constructions are based on a simple subset construction, do not involve intermediate automata with richer acceptance conditions, and can be implemented symbolically. We continue and solve the open problems of translating nondeterministic Streett, Rabin, Muller, and parity word automata to NCW and to DCW. Going via an intermediate NBW is not optimal and we describe direct, simple, and asymptotically tight constructions, involving a 2o(n) blow-up. The constructions are variants of the subset construction, providing a unified approach for translating all common classes of automata to NCW and DCW. Beyond the theoretical importance of the results, we point to numerous applications of the new constructions. In particular, they imply a simple subset-construction based translation, when possible, of LTL to deterministic Büchi word automata.},
  author       = {Boker, Udi and Kupferman, Orna},
  journal      = {ACM Transactions on Computational Logic},
  number       = {4},
  publisher    = {ACM},
  title        = {{Translating to Co-Büchi made tight, unified, and useful}},
  doi          = {10.1145/2362355.2362357},
  volume       = {13},
  year         = {2012},
}

@inproceedings{10905,
  abstract     = {Energy games belong to a class of turn-based two-player infinite-duration games played on a weighted directed graph. It is one of the rare and intriguing combinatorial problems that lie in NP ∩ co−NP, but are not known to be in P. While the existence of polynomial-time algorithms has been a major open problem for decades, there is no algorithm that solves any non-trivial subclass in polynomial time.
In this paper, we give several results based on the weight structures of the graph. First, we identify a notion of penalty and present a polynomial-time algorithm when the penalty is large. Our algorithm is the first polynomial-time algorithm on a large class of weighted graphs. It includes several counter examples that show that many previous algorithms, such as value iteration and random facet algorithms, require at least sub-exponential time. Our main technique is developing the first non-trivial approximation algorithm and showing how to convert it to an exact algorithm. Moreover, we show that in a practical case in verification where weights are clustered around a constant number of values, the energy game problem can be solved in polynomial time. We also show that the problem is still as hard as in general when the clique-width is bounded or the graph is strongly ergodic, suggesting that restricting graph structures need not help.},
  author       = {Chatterjee, Krishnendu and Henzinger, Monika H and Krinninger, Sebastian and Nanongkai, Danupon},
  booktitle    = {20th Annual European Symposium on Algorithms },
  isbn         = {9783642330896},
  issn         = {1611-3349},
  location     = {Ljubljana, Slovenia},
  pages        = {301--312},
  publisher    = {Springer},
  title        = {{Polynomial-time algorithms for energy games with special weight structures}},
  doi          = {10.1007/978-3-642-33090-2_27},
  volume       = {7501},
  year         = {2012},
}

@inproceedings{2891,
  abstract     = {Quantitative automata are nondeterministic finite automata with edge weights. They value a
run by some function from the sequence of visited weights to the reals, and value a word by its
minimal/maximal run. They generalize boolean automata, and have gained much attention in
recent years. Unfortunately, important automaton classes, such as sum, discounted-sum, and
limit-average automata, cannot be determinized. Yet, the quantitative setting provides the potential
of approximate determinization. We define approximate determinization with respect to
a distance function, and investigate this potential.
We show that sum automata cannot be determinized approximately with respect to any
distance function. However, restricting to nonnegative weights allows for approximate determinization
with respect to some distance functions.
Discounted-sum automata allow for approximate determinization, as the influence of a word’s
suffix is decaying. However, the naive approach, of unfolding the automaton computations up
to a sufficient level, is shown to be doubly exponential in the discount factor. We provide an
alternative construction that is singly exponential in the discount factor, in the precision, and
in the number of states. We prove matching lower bounds, showing exponential dependency on
each of these three parameters.
Average and limit-average automata are shown to prohibit approximate determinization with
respect to any distance function, and this is the case even for two weights, 0 and 1.},
  author       = {Boker, Udi and Henzinger, Thomas A},
  booktitle    = {Leibniz International Proceedings in Informatics},
  location     = {Hyderabad, India},
  pages        = {362 -- 373},
  publisher    = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
  title        = {{Approximate determinization of quantitative automata}},
  doi          = {10.4230/LIPIcs.FSTTCS.2012.362},
  volume       = {18},
  year         = {2012},
}

