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The complexity of the Hajós calculus for planar graphs

2010
*
Theoretical Computer Science
*

We prove that

doi:10.1016/j.tcs.2009.12.011
fatcat:yttqw24yprbvjbul7hgds2gcra
*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- ...##
###
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

2002
*
Discrete & Computational Geometry
*

We show that

doi:10.1007/s00454-001-0063-6
fatcat:cbhlvves75df7bj2njsjmi54qu
*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. ...##
###
Informationen – Die DMV – Impressum

2019
*
Mitteilungen der DMV
*

Dafinger, Markus: Invariant source forms, conservation laws and

doi:10.1515/dmvm-2019-0056
fatcat:tij3swmt3fcibg2tvpt5uc4oue
*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. ...##
###
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]

2004
*
Lecture Notes in Computer Science
*

Furthermore, we show that LA with quantification over permutations expresses NP graph-theoretic properties, and proves

doi:10.1007/978-3-540-27836-8_97
fatcat:5mc6qkfkwfettlxepnncxccelu
*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. ...##
###
LA, permutations, and the Hajós Calculus

2005
*
Theoretical Computer Science
*

Furthermore, we show that LA with quantification over permutations expresses NP graph-theoretic properties, and proves

doi:10.1016/j.tcs.2005.09.021
fatcat:f33uoja7bzgnxngj5rlhpdedoe
*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. ...##
###
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]

1998
*
arXiv
*
pre-print

For this purpose we identify

arXiv:quant-ph/9810069v1
fatcat:phzpo46ue5bkzlurhvoxs2ad2m
*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*...##
###
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
*

Obsah

*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. ...

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