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 in theory
 Anurag's Math Blog
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Recent Posts
 Incredibly awesome, but with overlength September 3, 2021
 Fields and total orders are the prime objects of nice categories January 30, 2021
 Prefixfree codes and ordinals May 11, 2020
 Isomorphism of labeled uniqueness trees April 20, 2020
 Defining a natural number as a finite string of digits is circular August 17, 2019
 Theory and practice of signeddigit representations April 16, 2019
 A list of books for understanding the nonrelativistic QM — Ajit R. Jadhav’s Weblog November 25, 2018
 I’m not a physicist April 29, 2018
 ALogTime, LogCFL, and threshold circuits: dreams of fast solutions November 2, 2017
 A subset interpretation (with context morphisms) of the sequent calculus for predicate logic September 24, 2017
 Logic without negation and falsehood December 11, 2016
 Logic without truth September 3, 2016
 Learning category theory: a necessary evil? April 3, 2016
 A canonical labeling technique by Brendan McKay and isomorphism testing of deterministic finite automata November 15, 2015
 On Zeros of a Polynomial in a Finite Grid: the AlonFuredi bound September 19, 2015
 Groupoids August 3, 2015
 Reversibility of binary relations, substochastic matrices, and partial functions March 22, 2015
 Algebraic characterizations of inverse semigroups and strongly regular rings December 6, 2014
 Gentzen’s consistency proof is more impressive than you expect December 5, 2013
Recent Comments
 Fields and total orders are the prime objects of nice categories  Gentzen translated on Defining a natural number as a finite string of digits is circular
 Fields and total orders are the prime objects of nice categories  Gentzen translated on Algebraic characterizations of inverse semigroups and strongly regular rings
 gentzen on ALogTime, LogCFL, and threshold circuits: dreams of fast solutions
 gentzen on Theory and practice of signeddigit representations
 gentzen on Defining a natural number as a finite string of digits is circular
 gentzen on Defining a natural number as a finite string of digits is circular
 gentzen on Theory and practice of signeddigit representations
 rjlipton on Theory and practice of signeddigit representations
 Defining a natural number as a finite string of digits is circular  Gentzen translated on Theory and practice of signeddigit representations
 Theory and practice of signeddigit representations  Gentzen translated on ALogTime, LogCFL, and threshold circuits: dreams of fast solutions
 Ajit R. Jadhav on A list of books for understanding the nonrelativistic QM — Ajit R. Jadhav’s Weblog
 gentzen on I’m not a physicist
 gentzen on ALogTime, LogCFL, and threshold circuits: dreams of fast solutions
 gentzen on ALogTime, LogCFL, and threshold circuits: dreams of fast solutions
 gentzen on ALogTime, LogCFL, and threshold circuits: dreams of fast solutions
Author Archives: gentzen
Incredibly awesome, but with overlength
Joel David Hamkins answering Daniel Rubin’s questions is incredible. I just had to write this post. Both are great, Joel is friendly and explains extremely well, and Daniel is direct, honest, and engaging in a funny way. And they really … Continue reading
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Fields and total orders are the prime objects of nice categories
A field is also a commutative ring, so it is an object in the category of commutative rings. A total order is also a partial order, so it is an object in the category of partially ordered sets. Neither are … Continue reading
Prefixfree codes and ordinals
Originally posted on What Immanuel Kant teach you:
Consider the problem of representing a number in computer memory, which is idealized as a sequence of zeros and ones. The binary number system is a wellknown solution to this problem —…
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Isomorphism of labeled uniqueness trees
The paper Deep Weisfeiler Leman by Martin Grohe, Pascal Schweitzer, Daniel Wiebking introduces a framework that allows the design of purely combinatorial graph isomorphism tests that are more powerful than the wellknown WeisfeilerLeman algorithm. This is a major achievement, see … Continue reading
Defining a natural number as a finite string of digits is circular
The length of a finite string is a natural number. If a given Turing machine halts on the empty input, then the number of steps it performs before halting is a natural number. (A Turing machine halts if it reaches … Continue reading
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Theory and practice of signeddigit representations
The integers are sometimes formally constructed as the equivalence classes of ordered pairs of natural numbers . The equivalence relation is defined via iff so that gets interpreted as . This motivates the signeddigit representation. To avoid storing two numbers … Continue reading
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A list of books for understanding the nonrelativistic QM — Ajit R. Jadhav’s Weblog
I really like that this post points out that QM is vast, and that it takes a prolonged, sustained effort to learn it. I also like that it explicitly recommends chemistry books. My own first exposure to the photoelectric effect … Continue reading
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I’m not a physicist
Background At the end of 2016, I decided to focus on working through an introductory textbook in quantum mechanics, instead of trying to make progress on my paper(s) to be published. I finished that textbook, which taught me things like … Continue reading
ALogTime, LogCFL, and threshold circuits: dreams of fast solutions
Our protagonists are the following (DLogTime) uniform circuit classes NC1 (ALogTime) SAC1 (LogCFL) TC0 (threshold circuits) Interesting things can be said about those classes. Things like Barrington’s theorem (NC1), closure under complementation by inductive counting (SAC1), or circuits for division … Continue reading
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A subset interpretation (with context morphisms) of the sequent calculus for predicate logic
The previous two posts used the sequent calculus with a subset interpretation: We work with sequents , and interpret the propositions (and ) as subsets of some universe set . We interpret the sequent itself as . While writing the … Continue reading