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» On Coalgebras over Algebras
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CSL
1997
Springer
13 years 11 months ago
Equational Axioms of Test Algebra
We present a complete axiomatization of test algebra ( 24, 18, 29]), the two-sorted algebraic variant of Propositional Dynamic Logic (PDL, 21, 7]). The axiomatization consists of ...
Marco Hollenberg
TPHOL
1999
IEEE
13 years 12 months ago
Universal Algebra in Type Theory
We present a development of Universal Algebra inside Type Theory, formalized using the proof assistant Coq. We define the notion of a signature and of an algebra over a signature. ...
Venanzio Capretta
FSTTCS
2009
Springer
14 years 2 months ago
The Power of Depth 2 Circuits over Algebras
We study the problem of polynomial identity testing (PIT) for depth 2 arithmetic circuits over matrix algebra. We show that identity testing of depth 3 (ΣΠΣ) arithmetic circuit...
Chandan Saha, Ramprasad Saptharishi, Nitin Saxena
LFCS
2009
Springer
14 years 2 months ago
Logic and Bounded-Width Rational Languages of Posets over Countable Scattered Linear Orderings
In this paper we consider languages of labelled N-free posets over countable and scattered linear orderings. We prove that a language of such posets is series-rational if and only ...
Nicolas Bedon
TAMC
2010
Springer
14 years 20 days ago
Algebraic Proofs over Noncommutative Formulas
We study possible formulations of algebraic propositional proof systems operating with noncommutative formulas. We observe that a simple formulation gives rise to systems at least ...
Iddo Tzameret