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The blog of Hector ZenilThu, 05 Jun 2014 04:17:57 +0000hourly1http://wordpress.org/?v=3.9.1Comment on On single and shortest axioms for Boolean logic by Doug Spoonwood
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Thu, 05 Jun 2014 04:17:57 +0000http://www.mathrix.org/liquid/?p=133#comment-67696I think for C* John meant to write CpCCqCprCqr p->((q->(p->r))->(q->r)).
]]>http://www.mathrix.org/liquid/archives/on-single-and-shortest-axioms/comment-page-1#comment-67696Comment on On single and shortest axioms for Boolean logic by Doug Spoonwood
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Sun, 04 May 2014 04:14:32 +0000http://www.mathrix.org/liquid/?p=133#comment-65179Does Tarski’s result imply that there exists a single axiom for systems with more than one connective like a conditional-conjunction positive logic? By the conditional-conjunction logic positive logic I mean a system which has theorems all derivable from the axiom set {CpCqp, CCpCqrCCpqCpr, CKpqp, CKpqq, CpCqKpq} under detachment and substitution. Does Tarski’s result imply there exists a single axiom for the full conditional conjunction logic (all theorems are derivable from {CpCqp, CCpCqrCCpqCpr, CCCpqpp, CKpqp, CKpqq, CpCqKpq})?
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Tue, 25 Mar 2014 20:26:06 +0000http://www.mathrix.org/liquid/?p=133#comment-63002Yes, thanks John, that is very interesting!
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Fri, 09 Aug 2013 10:27:49 +0000http://www.mathrix.org/liquid/?p=864#comment-53653That is indeed very interesting, but the paper only shows that the space growth for a dictionary attack on full sentences can be reduced by a linear factor (which in mathematical terms is next to nothing compared to the exponential growth). So my claim is still true even if in this paper and perhaps others they try to show that the strength does not go hand in hand with character growth given that sentences will follow some simple grammar rules, such as putting an adjective followed by a noun, which reduces the searching space of one and another. On top of that, I don’t think hackers get that sophisticated specially when it comes to personal passwords. Thanks!
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Fri, 09 Aug 2013 03:48:21 +0000http://www.mathrix.org/liquid/?p=864#comment-53647I think you’re mistaken when you say “to perform dictionary attacks over full sentences is computationally too expensive, so there is no way hackers can start doing so”.