Existence properties for first-order number theory are all finitely checkable
OK, that's a mouthful. I wrote an answer to How can I show that a function is not computable over at Quora, which brought up the Busy Beaver function. BB(n) is a typical example of a non-computable function.
TCS Walk Quarter Benefit At Rs. 8,126 Crore, Beats Examiners' Appraisals
Tata Consultancy Services (TCS) on Friday reported a net profit of Rs. 8,126 crore for the quarter ended March 31, 2019, beating analysts' estimates. That marked growth of 0.3 percent from its record net
TCS to drive blockchain technology
TCS to drive blockchain reception 1 min read . 14 Mar 2019 IANS The new TCS arrangements will utilize Microsoft Azure Blockchain Cloud TCS has been effectively conveying its "Quartz Blockchain
What does the AC0 complexity class mean?
AC^0 is a circuit complexity class. It represents the set of decision problems that are solvable with a family of constant-depth unlimited-fanin polynomial-size circuits. Photo by Yung Chang on Unsplash.
What makes any NP-complete problem also a PSPACE problem?
For any f(n), DTIME(f(n)) ⊆ SPACE(f(n)). This is because if you run for f(n) steps you can write to at most f(n) locations. (The reverse, of course, is not true.) The same applies for nondeterministic
An impractical reduction: factoring->3SAT->SUBSETSUM
The Subset Sum problem is NP-complete, but what does a reduction from another problem actually look like? I set out to create a concrete example. Let's start with factoring. What are the factors of 91?
Integers with low Kolmogorov complexity
I found this cute sequence in the Online Encyclopedia of Integer Sequences: A168650: Integers that can be generated with a C/C++ expression that is shorter than their decimal representation. The
Two Proofs of the Undecidability of the Halting Problem
The Halting Problem is whether or not a given Turing machine halts on a given input. This is the classic example of an undecidable problem, one that no Turing machine can accurately and completely solve.
Lower bounds on time complexity
I'm (slowly) continuing to read The Computational Complexity of Logical Theories, and it came in useful answering this Quora question: Can we predict [time] complexity before writing an algorithm? Here's
The Computational Complexity of Some Logical Theories
I'm reading a book from 1979 by Jeanne Ferrante and Charles W. Rackoff: "The Computational Complexity of Logical Theories." Though it's now nearly 40 years old, it still gets cited often, so