Turchin's Relation for Call-by-Name Computations: A Formal Approach

Supercompilation is a program transformation technique that was first described by V. F. Turchin in the 1970s. In supercompilation, Turchin's relation as a similarity relation on call-stack configurations is used both for call-by-value and call-by-name semantics to terminate unfolding of the program being transformed. In this paper, we give a formal grammar model of call-by-name stack behaviour. We classify the model in terms of the Chomsky hierarchy and then formally prove that Turchin's relation can terminate all computations generated by the model.Comment: In Proceedings VPT 2016, arXiv:1607.0183

RMS/Rate Dynamics via Localized Modes

We consider some reduction from nonlinear Vlasov-Maxwell equation to rms/rate equations for second moments related quantities. Our analysis is based on variational wavelet approach to rational (in dynamical variables) approximation. It allows to control contribution from each scale of underlying multiscales and represent solutions via multiscale exact nonlinear eigenmodes (waveletons) expansions. Our approach provides the possibility to work with well-localized bases in phase space and best convergence properties of the corresponding expansions without perturbations or/and linearization procedures.Comment: 4 pages, 2 figures, JAC2001.cls, presented at European Particle Accelerator Conference (EPAC02), Paris, June 3-7, 2002; changed from A4 to US format for correct printin

Approximating solution structure of the Weighted Sentence Alignment problem

We study the complexity of approximating solution structure of the bijective weighted sentence alignment problem of DeNero and Klein (2008). In particular, we consider the complexity of finding an alignment that has a significant overlap with an optimal alignment. We discuss ways of representing the solution for the general weighted sentence alignment as well as phrases-to-words alignment problem, and show that computing a string which agrees with the optimal sentence partition on more than half (plus an arbitrarily small polynomial fraction) positions for the phrases-to-words alignment is NP-hard. For the general weighted sentence alignment we obtain such bound from the agreement on a little over 2/3 of the bits. Additionally, we generalize the Hamming distance approximation of a solution structure to approximating it with respect to the edit distance metric, obtaining similar lower bounds

Classical and Quantum Ensembles via Multiresolution. II. Wigner Ensembles

We present the application of the variational-wavelet analysis to the analysis of quantum ensembles in Wigner framework. (Naive) deformation quantization, the multiresolution representations and the variational approach are the key points. We construct the solutions of Wigner-like equations via the multiscale expansions in the generalized coherent states or high-localized nonlinear eigenmodes in the base of the compactly supported wavelets and the wavelet packets. We demonstrate the appearance of (stable) localized patterns (waveletons) and consider entanglement and decoherence as possible applications.Comment: 5 pages, 2 figures, espcrc2.sty, Presented at IX International Workshop on Advanced Computing and Analysis Techniques in Physics Research, Section III "Simulations and Computations in Theoretical Physics and Phenomenology", ACAT 2003, December, 2003, KEK, Tsukub