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

Multi-Gigabit Wireless data transfer at 60 GHz

In this paper we describe the status of the first prototype of the 60 GHz wireless Multi-gigabit data transfer topology currently under development at University of Heidelberg using IBM 130 nm SiGe HBT BiCMOS technology. The 60 GHz band is very suitable for high data rate and short distance applications as for example needed in the HEP experments. The wireless transceiver consist of a transmitter and a receiver. The transmitter includes an On-Off Keying (OOK) modulator, an Local Oscillator (LO), a Power Amplifier (PA) and a BandPass Filter (BPF). The receiver part is composed of a BandPass- Filter (BPF), a Low Noise Amplifier (LNA), a double balanced down-convert Gilbert mixer, a Local Oscillator (LO), then a BPF to remove the mixer introduced noise, an Intermediate Amplifier (IF), an On-Off Keying demodulator and a limiting amplifier. The first prototype would be able to handle a data-rate of about 3.5 Gbps over a link distance of 1 m. The first simulations of the LNA show that a Noise Figure (NF) of 5 dB, a power gain of 21 dB at 60 GHz with a 3 dB bandwidth of more than 20 GHz with a power consumption 11 mW are achieved. Simulations of the PA show an output referred compression point P1dB of 19.7 dB at 60 GHz.Comment: Proceedings of the WIT201

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

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

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