Breaking the PPSZ Barrier for Unique 3-SAT

The PPSZ algorithm by Paturi, Pudl\'ak, Saks, and Zane (FOCS 1998) is the fastest known algorithm for (Promise) Unique k-SAT. We give an improved algorithm with exponentially faster bounds for Unique 3-SAT. For uniquely satisfiable 3-CNF formulas, we do the following case distinction: We call a clause critical if exactly one literal is satisfied by the unique satisfying assignment. If a formula has many critical clauses, we observe that PPSZ by itself is already faster. If there are only few clauses allover, we use an algorithm by Wahlstr\"om (ESA 2005) that is faster than PPSZ in this case. Otherwise we have a formula with few critical and many non-critical clauses. Non-critical clauses have at least two literals satisfied; we show how to exploit this to improve PPSZ.Comment: 13 pages; major revision with simplified algorithm but slightly worse constant

Hardness of Sparse Sets and Minimal Circuit Size Problem

We develop a polynomial method on finite fields to amplify the hardness of spare sets in nondeterministic time complexity classes on a randomized streaming model. One of our results shows that if there exists a $2^{n^{o(1)}}$-sparse set in $NTIME(2^{n^{o(1)}})$ that does not have any randomized streaming algorithm with $n^{o(1)}$ updating time, and $n^{o(1)}$ space, then $NEXP\not=BPP$, where a $f(n)$-sparse set is a language that has at most $f(n)$ strings of length $n$. We also show that if MCSP is $ZPP$-hard under polynomial time truth-table reductions, then $EXP\not=ZPP$

"Boring formal methods" or "Sherlock Holmes deduction methods"?

This paper provides an overview of common challenges in teaching of logic and formal methods to Computer Science and IT students. We discuss our experiences from the course IN3050: Applied Logic in Engineering, introduced as a "logic for everybody" elective course at at TU Munich, Germany, to engage pupils studying Computer Science, IT and engineering subjects on Bachelor and Master levels. Our goal was to overcome the bias that logic and formal methods are not only very complicated but also very boring to study and to apply. In this paper, we present the core structure of the course, provide examples of exercises and evaluate the course based on the students' surveys.Comment: Preprint. Accepted to the Software Technologies: Applications and Foundations (STAF 2016). Final version published by Springer International Publishing AG. arXiv admin note: substantial text overlap with arXiv:1602.0517

Electric-dipole active two-magnon excitation in {\textit{ab}} spiral spin phase of a ferroelectric magnet Gd0.7_{\textbf{0.7}}Tb0.3_{\textbf{0.3}}MnO3_{\textbf 3}

A broad continuum-like spin excitation (1--10 meV) with a peak structure around 2.4 meV has been observed in the ferroelectric $ab$ spiral spin phase of Gd$_{0.7}$Tb$_{0.3}$MnO$_3$ by using terahertz (THz) time-domain spectroscopy. Based on a complete set of light-polarization measurements, we identify the spin excitation active for the light $E$ vector only along the a-axis, which grows in intensity with lowering temperature even from above the magnetic ordering temperature but disappears upon the transition to the $A$-type antiferromagnetic phase. Such an electric-dipole active spin excitation as observed at THz frequencies can be ascribed to the two-magnon excitation in terms of the unique polarization selection rule in a variety of the magnetically ordered phases.Comment: 11 pages including 3 figure

Faster transport with a directed quantum walk

We give the first example of faster transport with a quantum walk on an inherently directed graph, on the directed line with a variable number of self-loops at each vertex. These self-loops can be thought of as adding a number of small dimensions. This is a discrete time quantum walk using the Fourier transform coin, where the walk proceeds a distance $\Theta(1)$ in constant time compared to $\Theta(1/n)$ classically, independent of the number of these small dimensions. The analysis proceeds by reducing this walk to a walk with a two dimensional coin.Comment: 3 pages, 2 figures. To be published in Phys. Rev. A. v2: Minor wording changes. For Mathematica simulation source, see http://panic.berkeley.edu/~shoyer

Nominal Unification of Higher Order Expressions with Recursive Let

A sound and complete algorithm for nominal unification of higher-order expressions with a recursive let is described, and shown to run in non-deterministic polynomial time. We also explore specializations like nominal letrec-matching for plain expressions and for DAGs and determine the complexity of corresponding unification problems.Comment: Pre-proceedings paper presented at the 26th International Symposium on Logic-Based Program Synthesis and Transformation (LOPSTR 2016), Edinburgh, Scotland UK, 6-8 September 2016 (arXiv:1608.02534

P-Selectivity, Immunity, and the Power of One Bit

We prove that P-sel, the class of all P-selective sets, is EXP-immune, but is not EXP/1-immune. That is, we prove that some infinite P-selective set has no infinite EXP-time subset, but we also prove that every infinite P-selective set has some infinite subset in EXP/1. Informally put, the immunity of P-sel is so fragile that it is pierced by a single bit of information. The above claims follow from broader results that we obtain about the immunity of the P-selective sets. In particular, we prove that for every recursive function f, P-sel is DTIME(f)-immune. Yet we also prove that P-sel is not \Pi_2^p/1-immune

Making Gestural Interaction Accessible to Visually Impaired People

International audienceAs touch screens become widely spread, making them more accessible to visually impaired people is an important task. Touch displays possess a poor accessibility for visually impaired people. One possibility to make them more accessible without sight is through gestural interaction. Yet, there are still few studies on using gestural interaction for visually impaired people. In this paper we present a comprehensive summary of existing projects investigating accessible gestural interaction. We also highlight the limits of current approaches and propose future working directions. Then, we present the design of an interactive map prototype that includes both a raised-line map overlay and gestural interaction for accessing different types of information (e.g., opening hours, distances). Preliminary results of our project show that basic gestural interaction techniques can be successfully used in interactive maps for visually impaired people

MuPix7 - A fast monolithic HV-CMOS pixel chip for Mu3e

The MuPix7 chip is a monolithic HV-CMOS pixel chip, thinned down to 50 \mu m. It provides continuous self-triggered, non-shuttered readout at rates up to 30 Mhits/chip of 3x3 mm^2 active area and a pixel size of 103x80 \mu m^2. The hit efficiency depends on the chosen working point. Settings with a power consumption of 300 mW/cm^2 allow for a hit efficiency >99.5%. A time resolution of 14.2 ns (Gaussian sigma) is achieved. Latest results from 2016 test beam campaigns are shown.Comment: Proceedingsfor the PIXEL2016 conference, submitted to JINST A dangling reference has been removed from this version, no other change

Unary Pushdown Automata and Straight-Line Programs

We consider decision problems for deterministic pushdown automata over a unary alphabet (udpda, for short). Udpda are a simple computation model that accept exactly the unary regular languages, but can be exponentially more succinct than finite-state automata. We complete the complexity landscape for udpda by showing that emptiness (and thus universality) is P-hard, equivalence and compressed membership problems are P-complete, and inclusion is coNP-complete. Our upper bounds are based on a translation theorem between udpda and straight-line programs over the binary alphabet (SLPs). We show that the characteristic sequence of any udpda can be represented as a pair of SLPs---one for the prefix, one for the lasso---that have size linear in the size of the udpda and can be computed in polynomial time. Hence, decision problems on udpda are reduced to decision problems on SLPs. Conversely, any SLP can be converted in logarithmic space into a udpda, and this forms the basis for our lower bound proofs. We show coNP-hardness of the ordered matching problem for SLPs, from which we derive coNP-hardness for inclusion. In addition, we complete the complexity landscape for unary nondeterministic pushdown automata by showing that the universality problem is $\Pi_2 \mathrm P$-hard, using a new class of integer expressions. Our techniques have applications beyond udpda. We show that our results imply $\Pi_2 \mathrm P$-completeness for a natural fragment of Presburger arithmetic and coNP lower bounds for compressed matching problems with one-character wildcards