VPSPACE and a transfer theorem over the complex field

We extend the transfer theorem of [KP2007] to the complex field. That is, we investigate the links between the class VPSPACE of families of polynomials and the Blum-Shub-Smale model of computation over C. Roughly speaking, a family of polynomials is in VPSPACE if its coefficients can be computed in polynomial space. Our main result is that if (uniform, constant-free) VPSPACE families can be evaluated efficiently then the class PAR of decision problems that can be solved in parallel polynomial time over the complex field collapses to P. As a result, one must first be able to show that there are VPSPACE families which are hard to evaluate in order to separate P from NP over C, or even from PAR.Comment: 14 page

Approximating Fractional Time Quantum Evolution

An algorithm is presented for approximating arbitrary powers of a black box unitary operation, $\mathcal{U}^t$, where $t$ is a real number, and $\mathcal{U}$ is a black box implementing an unknown unitary. The complexity of this algorithm is calculated in terms of the number of calls to the black box, the errors in the approximation, and a certain `gap' parameter. For general $\mathcal{U}$ and large $t$, one should apply $\mathcal{U}$ a total of $\lfloor t \rfloor$ times followed by our procedure for approximating the fractional power $\mathcal{U}^{t-\lfloor t \rfloor}$. An example is also given where for large integers $t$ this method is more efficient than direct application of $t$ copies of $\mathcal{U}$. Further applications and related algorithms are also discussed.Comment: 13 pages, 2 figure

On-line hand-drawn electric circuit diagram recognition using 2D dynamic programming

9 pagesInternational audienceIn order to facilitate sketch recognition, most online existing works assume that people will not start to draw a new symbol before the current one has been finished. We propose in this paper a method that relaxes this constraint. The proposed methodology relies on a two-dimensional dynamic programming (2D-DP) technique allowing symbol hypothesis generation, which can correctly segment and recognize interspersed symbols. In addition, as discriminative classifiers usually have limited capability to reject outliers, some domain specific knowledge is included to circumvent those errors due to untrained patterns corresponding to erroneous segmentation hypotheses. With a point-level measurement, the experiment shows that the proposed novel approach is able to achieve an accuracy of more than 90 percent

A natural interaction reasoning system for electronic circuit analysis in an educational setting

Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.Includes bibliographical references (p. 42).This thesis presents a sketch-based interaction system that can be used to illustrate the process of reasoning about an electrical circuit in an educational setting. Recognition of hand-drawn shapes is accomplished in a two stage process where strokes are first processed into primitives like lines or ellipses, then combined into the appropriate circuit device symbols using a shape description language called LADDER. The circuit is then solved by a constraint-propagation reasoning component. The solution is shown to the user along with the justifications that support each deduction. The level of detail and the speed of the solution playback can be customized to tailor to a student's particular learning pace. A small user study was conducted to test the performance of the recognition component, which revealed several recognition problems common to almost all of the users' experiences with the system. Suggestions for dealing with these problems are also presented.by Chang She.M.Eng

On space efficiency of algorithms working on structural decompositions of graphs

Dynamic programming on path and tree decompositions of graphs is a technique that is ubiquitous in the field of parameterized and exponential-time algorithms. However, one of its drawbacks is that the space usage is exponential in the decomposition's width. Following the work of Allender et al. [Theory of Computing, '14], we investigate whether this space complexity explosion is unavoidable. Using the idea of reparameterization of Cai and Juedes [J. Comput. Syst. Sci., '03], we prove that the question is closely related to a conjecture that the Longest Common Subsequence problem parameterized by the number of input strings does not admit an algorithm that simultaneously uses XP time and FPT space. Moreover, we complete the complexity landscape sketched for pathwidth and treewidth by Allender et al. by considering the parameter tree-depth. We prove that computations on tree-depth decompositions correspond to a model of non-deterministic machines that work in polynomial time and logarithmic space, with access to an auxiliary stack of maximum height equal to the decomposition's depth. Together with the results of Allender et al., this describes a hierarchy of complexity classes for polynomial-time non-deterministic machines with different restrictions on the access to working space, which mirrors the classic relations between treewidth, pathwidth, and tree-depth.Comment: An extended abstract appeared in the proceedings of STACS'16. The new version is augmented with a space-efficient algorithm for Dominating Set using the Chinese remainder theore

Frege systems for quantified Boolean logic

We define and investigate Frege systems for quantified Boolean formulas (QBF). For these new proof systems, we develop a lower bound technique that directly lifts circuit lower bounds for a circuit class C to the QBF Frege system operating with lines from C. Such a direct transfer from circuit to proof complexity lower bounds has often been postulated for propositional systems but had not been formally established in such generality for any proof systems prior to this work. This leads to strong lower bounds for restricted versions of QBF Frege, in particular an exponential lower bound for QBF Frege systems operating with AC0[p] circuits. In contrast, any non-trivial lower bound for propositional AC0[p]-Frege constitutes a major open problem. Improving these lower bounds to unrestricted QBF Frege tightly corresponds to the major problems in circuit complexity and propositional proof complexity. In particular, proving a lower bound for QBF Frege systems operating with arbitrary P/poly circuits is equivalent to either showing a lower bound for P/poly or for propositional extended Frege (which operates with P/poly circuits). We also compare our new QBF Frege systems to standard sequent calculi for QBF and establish a correspondence to intuitionistic bounded arithmetic.This research was supported by grant nos. 48138 and 60842 from the John Templeton Foundation, EPSRC grant EP/L024233/1, and a Doctoral Prize Fellowship from EPSRC (third author). The second author was funded by the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007–2013)/ERC grant agreement no. 279611 and under the European Union’s Horizon 2020 Research and Innovation Programme/ERC grant agreement no. 648276 AUTAR. The fourth author was supported by the Austrian Science Fund (FWF) under project number P28699 and by the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2014)/ERC Grant Agreement no. 61507. Part of this work was done when Beyersdorff and Pich were at the University of Leeds and Bonacina at Sapienza University Rome.Peer ReviewedPostprint (published version

Synthesis of Computable Regular Functions of Infinite Words

Regular functions from infinite words to infinite words can be equivalently specified by MSO-transducers, streaming ?-string transducers as well as deterministic two-way transducers with look-ahead. In their one-way restriction, the latter transducers define the class of rational functions. Even though regular functions are robustly characterised by several finite-state devices, even the subclass of rational functions may contain functions which are not computable (by a Turing machine with infinite input). This paper proposes a decision procedure for the following synthesis problem: given a regular function f (equivalently specified by one of the aforementioned transducer model), is f computable and if it is, synthesize a Turing machine computing it. For regular functions, we show that computability is equivalent to continuity, and therefore the problem boils down to deciding continuity. We establish a generic characterisation of continuity for functions preserving regular languages under inverse image (such as regular functions). We exploit this characterisation to show the decidability of continuity (and hence computability) of rational and regular functions. For rational functions, we show that this can be done in NLogSpace (it was already known to be in PTime by Prieur). In a similar fashion, we also effectively characterise uniform continuity of regular functions, and relate it to the notion of uniform computability, which offers stronger efficiency guarantees

CONTREX: Design of embedded mixed-criticality CONTRol systems under consideration of EXtra-functional properties

The increasing processing power of today’s HW/SW platforms leads to the integration of more and more functions in a single device. Additional design challenges arise when these functions share computing resources and belong to different criticality levels. CONTREX complements current activities in the area of predictable computing platforms and segregation mechanisms with techniques to consider the extra-functional properties, i.e., timing constraints, power, and temperature. CONTREX enables energy efficient and cost aware design through analysis and optimization of these properties with regard to application demands at different criticality levels. This article presents an overview of the CONTREX European project, its main innovative technology (extension of a model based design approach, functional and extra-functional analysis with executable models and run-time management) and the final results of three industrial use-cases from different domain (avionics, automotive and telecommunication).The work leading to these results has received funding from the European Community’s Seventh Framework Programme FP7/2007-2011 under grant agreement no. 611146