Using Middle-Out Reasoning to Control the Synthesis of Tail-Recursive Programs

We describe a novel technique for the automatic synthesis of tail-recursive programs. The technique is to specify the required program using the standard equations and then synthesise the tail-recursive program using the proofs as programs technique. This requires the specification to be proved realisable in a constructive logic. Restrictions on the form of the proof ensure that the synthesised program is tail-recursive. Th

Symbolic Algorithms for Language Equivalence and Kleene Algebra with Tests

We first propose algorithms for checking language equivalence of finite automata over a large alphabet. We use symbolic automata, where the transition function is compactly represented using a (multi-terminal) binary decision diagrams (BDD). The key idea consists in computing a bisimulation by exploring reachable pairs symbolically, so as to avoid redundancies. This idea can be combined with already existing optimisations, and we show in particular a nice integration with the disjoint sets forest data-structure from Hopcroft and Karp's standard algorithm. Then we consider Kleene algebra with tests (KAT), an algebraic theory that can be used for verification in various domains ranging from compiler optimisation to network programming analysis. This theory is decidable by reduction to language equivalence of automata on guarded strings, a particular kind of automata that have exponentially large alphabets. We propose several methods allowing to construct symbolic automata out of KAT expressions, based either on Brzozowski's derivatives or standard automata constructions. All in all, this results in efficient algorithms for deciding equivalence of KAT expressions

Quantum Measurements and the kappa--Poincare Group

The possible description of the vacuum of quantum gravity through the so called kappa--Poincare group is analyzed considering some of the consequences of this symmetry in the path integral formulation of nonrelativistic quantum theory. This study is carried out with two cases, firstly, a free particle, and finally, the situation of a particle immersed in a homogeneous gravitational field. It will be shown that the kappa--Poincare group implies the loss of some of the basic properties associated to Feynman's path integral. For instance, loss of the group characteristic related to the time dependence of the evolution operator, or the breakdown of the composition law for amplitudes of events occurring successively in time. Additionally some similarities between the present idea and the so called restricted path integral formalism will be underlined. These analogies advocate the claim that if the kappa--Poincare group contains some of the physical information of the quantum gravity vacuum, then this vacuum could entail decoherence. This last result will also allow us to consider the possibility of analyzing the continuous measurement problem of quantum theory from a group--theoretical point of view, but now taking into account the kappa--Poincare symmetries.Comment: Accepted in General Relativity and Gravitation. Dedicated to Alberto Garcia on the occasion of his 60th. birthda

Testing the ΔS=ΔQ\Delta S=\Delta Q Rule with Exclusive Semi-Leptonic Kaon Decays

We consider the possibility of violations of the selection rule $\Delta S=\Delta Q$ at an appreciable level in {\it exclusive} semi-leptonic decays of Kaons. At $\Phi$-Factories, intense Kaon beams will be available and will probe among others, the semi-leptonic decays $K_{l4}$ and $K_{l3\gamma}$ in addition to $K_{l3}$ and could provide novel testing grounds for the $\Delta S=\Delta Q$ rule. In particular, the branching ratio of $K_{l3\gamma}$ is non-negligible and could be used to probe new phenomena associated with the violation of this selection rule. Furthermore, we modify certain di-lepton event rate ratios and asymmetries and time asymmetries that have been constructed by Dass and Sarma for di-lepton events from Beon decays to test the $\Delta B=\Delta Q$ at the $\Upsilon (4S)$, to the Kaon system at the $\phi(1020)$. We find that the large width of the $K_S$ relative to that of $K_L$ plays an important role in enhancing some of the time asymmetries.Comment: 10 pages, Plain Latex, To be run twice

Effect of reheating on electroweak baryogenesis

The latent heat released during the expansion of bubbles in the electroweak phase transition reheats the plasma and causes the bubble growth to slow down. This decrease of the bubble wall velocity affects the result of electroweak baryogenesis. Since the efficiency of baryogenesis peaks for a wall velocity $\sim 10^{-2}$, the resulting baryon asymmetry can either be enhanced or suppressed, depending on the initial value of the wall velocity. We calculate the evolution of the phase transition taking into account the release of latent heat. We find that, although in the SM the baryon production is enhanced by this effect, in the MSSM it causes a suppression to the final baryon asymmetry.Comment: 4 pages, 3 figures. References added. Revised version to be published in Phys.Rev.

Electroweak Baryogenesis and Standard Model CP Violation

We analyze the mechanism of electroweak baryogenesis proposed by Farrar and Shaposhnikov in which the phase of the CKM mixing matrix is the only source of $CP$ violation. This mechanism is based on a phase separation of baryons via the scattering of quasiparticles by the wall of an expanding bubble produced at the electroweak phase transition. In agreement with the recent work of Gavela, Hern\'andez, Orloff and P\`ene, we conclude that QCD damping effects reduce the asymmetry produced to a negligible amount. We interpret the damping as quantum decoherence. We compute the asymmetry analytically. Our analysis reflects the observation that only a thin, outer layer of the bubble contributes to the coherent scattering of the quasiparticles. The generality of our arguments rules out any mechanism of electroweak baryogenesis that does not make use of a new source of $CP$ violation.Comment: 36 pages, in LaTeX, one LaTeX figure included, 5 others available upon request, SLAC-PUB-647

Heavily-doped Germanium on Silicon with Activated Doping Exceeding 1020 cm−3 as an Alternative to Gold for Mid-infrared Plasmonics

Ge-on-Si has been demonstrated as a platform for Si foundry compatible plasmonics. We use laser thermal annealing to demonstrate activated doping levels >1020 cm-3 which allows most of the 3 to 20 μm mid-infrared sensing window to be covered with enhancements comparable to gold plasmonics

A standardisation proof for algebraic pattern calculi

This work gives some insights and results on standardisation for call-by-name pattern calculi. More precisely, we define standard reductions for a pattern calculus with constructor-based data terms and patterns. This notion is based on reduction steps that are needed to match an argument with respect to a given pattern. We prove the Standardisation Theorem by using the technique developed by Takahashi and Crary for lambda-calculus. The proof is based on the fact that any development can be specified as a sequence of head steps followed by internal reductions, i.e. reductions in which no head steps are involved.Comment: In Proceedings HOR 2010, arXiv:1102.346

Quantum theory's last challenge

Quantum mechanics is now 100 years old and still going strong. Combining general relativity with quantum mechanics is the last hurdle to be overcome in the "quantum revolution".Comment: (9 pages, LaTex) This is the preprint version of an article that appeared in the issue 6813 (volume 408) of Nature, as part of a 3-article celebration of the 100th anniversary of Planck's solution of the black-body-radiation proble