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The complexity of the Hajós calculus for planar graphs

Kazuo Iwama, Kazuhisa Seto, Suguru Tamaki
2010 Theoretical Computer Science  
We prove that the planar Hajós calculus is polynomially bounded iff the Hajós calculus is polynomially bounded.  ...  The planar Hajós calculus is the Hajós calculus with the restriction that all the graphs that appear in the construction (including a final graph) must be planar.  ...  Nevertheless we prove that the worst-case complexity of the planar Hajós calculus is polynomially equivalent to that of the general Hajós calculus, i.e., the former is polynomially bounded for all non-  ... 
doi:10.1016/j.tcs.2009.12.011 fatcat:yttqw24yprbvjbul7hgds2gcra

Page 5020 of Mathematical Reviews Vol. , Issue 96h [page]

1996 Mathematical Reviews  
We also establish a relationship between a complete subsystem of the Hajos calculus and bounded-depth Frege systems; this enables us to prove exponential lower bounds on this subsystem of the Hajos calculus  ...  Summary: “The Hajos calculus is a simple, nondeterministic pro- cedure that generates the class of non-3-colorable graphs.  ... 

Page 1797 of Mathematical Reviews Vol. , Issue 96c [page]

1996 Mathematical Reviews  
Summary: “The Hajos calculus is a simple, nondeterministic procedure which generates precisely the class of non-3-colorable graphs.  ...  In this note, we prove exponential lower bounds on the size of tree-like Hajos constructions.” 96c:68063 68Q15 Juedes, David W. (1-IASU-C; Ames, IA); Lutz, Jack H. (1-I[ASU-C; Ames, IA) The complexity  ... 

Page 1089 of Mathematical Reviews Vol. , Issue 96b [page]

1996 Mathematical Reviews  
Turing machine (30-36); Kazuo Iwama, Non-polynomial time boundedness of the tree-like Hajos calculus (37-44); Kenichi Morita, Yasunori Yamamoto, Noritaka Nishihara and Zhiguo Zhang, Uniquely parsable  ...  |Computational complexity theory] Proceedings of a conference held at the Research Institute for Mathematical Sciences, Kyoto University, Kyoto, February 1-3, 1994.  ... 

A Dido Problem as Modernized by Fejes Tóth

A. Siegel
2002 Discrete & Computational Geometry  
We show that the area of the enclosed region is maximal precisely when the arrangement of segments defines a simple polygon that satisfies a fundamental isoperimetric inequality, and thereby answer the  ...  Let a finite number of line segments be located in the plane. Let C be a circle that surrounds the segments.  ...  Part of the proof's simplicity comes from the use of divide and conquer to reduce the complexity imposed by a morass of arbitrarily placed segments.  ... 
doi:10.1007/s00454-001-0063-6 fatcat:cbhlvves75df7bj2njsjmi54qu

Informationen – Die DMV – Impressum

2019 Mitteilungen der DMV  
Dafinger, Markus: Invariant source forms, conservation laws and the inverse problem of the calculus of variations. Grieser, Andersen ...  ...  Krautenbacher, Norbert: Learning on complex, biased, and big data: Disease risk prediction in epidemiological studies and genomic medicine on the example of childhood asthma.  ... 
doi:10.1515/dmvm-2019-0056 fatcat:tij3swmt3fcibg2tvpt5uc4oue

Page 3166 of Mathematical Reviews Vol. , Issue 96e [page]

1996 Mathematical Reviews  
A differential calculus is constructed on the discrete space M4 x Z2, in a way similar though not identical to the formalism of A. Sitarz [J. Geom.  ...  The differential calculus previously constructed by the authors on the discrete space M, x Z, is generalized to the space My x Zy.  ... 

Page 3701 of Mathematical Reviews Vol. , Issue 95f [page]

1995 Mathematical Reviews  
Summary: “We present a canonical method for solving one- dimensional linear. differential equations, making use of pseu- dodifferential calculus.  ...  (CL-UNC-P; Bogota) Application of complex canonical point transformations to linear second-order differential equations. (English summary) J. Phys. A 26 (1993), no. 21, 5937-5952.  ... 

Page 7276 of Mathematical Reviews Vol. , Issue 97M [page]

1997 Mathematical Reviews  
Sheftel’], Theorems on isomorphism for general elliptic problems with a shift (364-368); Mikhail Smirnov, Radon transforms, symplectic geometry and inverse problem of geometric calculus of variations (  ...  Mercik, Lévy-stable and extreme value distributions in modelling of dynamical phenomena in complex physical systems (545-558); J. Zakrzewski, K. Dupret and D.  ... 

LA, Permutations, and the Hajós Calculus [chapter]

Michael Soltys
2004 Lecture Notes in Computer Science  
Furthermore, we show that LA with quantification over permutations expresses NP graph-theoretic properties, and proves the soundness of the Hajós Calculus. Several open problems are stated.  ...  We show that LA, over finite fields, proves a host of matrix identities (so called "hard matrix identities") from the matrix form of the pigeonhole principle.  ...  The author would like to thank Toniann Pitassi and Alasdair Urquhart for fruitful discussions that led to this paper.  ... 
doi:10.1007/978-3-540-27836-8_97 fatcat:5mc6qkfkwfettlxepnncxccelu

LA, permutations, and the Hajós Calculus

Michael Soltys
2005 Theoretical Computer Science  
Furthermore, we show that LA with quantification over permutations expresses NP graph-theoretic properties, and proves the soundness of the Hajós Calculus. Several open problems are stated.  ...  We show that LA, over finite fields, proves a host of matrix identities (so called "hard matrix identities") from the matrix form of the pigeonhole principle.  ...  The author would like to thank Toniann Pitassi and Alasdair Urquhart for fruitful discussions that led to this paper.  ... 
doi:10.1016/j.tcs.2005.09.021 fatcat:f33uoja7bzgnxngj5rlhpdedoe

Page 7265 of Mathematical Reviews Vol. , Issue 98K [page]

1998 Mathematical Reviews  
Song, Efficient paral- lel graph algorithms for coarse grained multicomputers and BSP (390-400); Andris Ambainis, Upper bound on the communica- tion complexity of private information retrieval (401-407  ...  ); David Harel and Eli Singerman, Computation paths logic: an expressive, yet elementary, process logic (abridged version) (408-418); Olaf Burkart and Bernhard Steffen, Model checking the full modal mu-calculus  ... 

A rigorous path-integral formula for quantum-spin dynamics via planar Brownian motion [article]

Bernhard Bodmann, Hajo Leschke, Simone Warzel
1998 arXiv   pre-print
For this purpose we identify the finite-dimensional spin Hilbert space with the ground-state eigenspace of a suitable Schödinger operator on L^2(R^2), the Hilbert space of square-integrable functions on  ...  Adapting ideas of Daubechies and Klauder we derive a continuum path-integral formula for the time evolution generated by a spin Hamiltonian.  ...  rules of ordinary calculus, although the time derivative . b does not exist. 9 Several comments apply: • In order to make contact with the Wiener-regularized path-integral expression associated with the  ... 
arXiv:quant-ph/9810069v1 fatcat:phzpo46ue5bkzlurhvoxs2ad2m

Page 5169 of Mathematical Reviews Vol. , Issue 2000g [page]

2000 Mathematical Reviews  
Saririan, Complex monopoles in the path integral (287-290); B. Kuckert, A short cut towards spin & statistics (299-302); G.  ...  Fleischhauer, Regular- isations and stochastic calculus (241-244); J. Polonyi, Path integral for the Dirac equation (245-248); L. V. Prokhorov, On motion in curved spaces (249-252); E. T.  ... 

Contents
Obsah

1949 Časopis pro pěstování mathematiky a fysiky  
of numbers as applied to the propositional calculus.  ...  -O některých zjednodušeních von Neumannovy axiomatické theorie množin 14Ž Josef Novák, Praha: On the ordered continua of the power 2**° containing a dense subset of the power **.  ...  Halina Milicer-Gružewska, Warszawa: The approximatíon of the limit probability law. -Aproksymacja prawa granicznego 281 Jaroslav Hájek, Praha: Representativní vyber skupin methodou dvou fází.  ... 
doi:10.21136/cpmf.1949.122480 fatcat:vwrgsjtjpjafjlhvsdgnteukk4
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