Add to ORKGFrom algorithmic information theory (and using notions of algorithmic thermodynamics), we introduce *feasible mathematics* as distinct from *universal mathematics*. Feasible mathematics formalizes the intuition that theorems with very long proofs are unprovable within the context of limited computing resources. It is formalized by augmenting the standard construction of Omega with a conjugate-pair that suppresses programs with long runtimes. The domain of the new construction defines feasible mathematics
Information theory is a branch of mathematics that attempts to quantify information. To quantify inf...
Investigating Logics for Feasible Computation The most celebrated open problem in theoretical comput...
In recent years, classical computability has expanded beyond its original scope to address issues re...
From algorithmic information theory (and using notions of algorithmic thermodynamics), we introduce ...
From algorithmic information theory (and using notions of algorithmic thermodynamics), we introduce ...
A so-called "effective" algorithm may require arbitrarily large finite amounts of time and space res...
Perspicuity is part of proof. If the process by means of which I get a result were not surveyable, I...
Why do we need a formalization of the notion of algorithm or effective computation? In order to show...
Why do we need a formalization of the notion of algorithm or effective computation? In order to show...
Why do we need a formalization of the notion of algorithm or effective computation? In order to show...
The goal of this chapter is to bring to the attention of philosophers of mathematics the concept of ...
During the last four years research on the lower level computational complexity has yielded a rich s...
We provide a new proof of the fact that Mathematical Programming is Turing-complete, and show how it...
We provide a new proof of the fact that Mathematical Programming is Turing-complete, and show how it...
We provide a new proof of the fact that Mathematical Programming is Turing-complete, and show how it...
Information theory is a branch of mathematics that attempts to quantify information. To quantify inf...
Investigating Logics for Feasible Computation The most celebrated open problem in theoretical comput...
In recent years, classical computability has expanded beyond its original scope to address issues re...
From algorithmic information theory (and using notions of algorithmic thermodynamics), we introduce ...
From algorithmic information theory (and using notions of algorithmic thermodynamics), we introduce ...
A so-called "effective" algorithm may require arbitrarily large finite amounts of time and space res...
Perspicuity is part of proof. If the process by means of which I get a result were not surveyable, I...
Why do we need a formalization of the notion of algorithm or effective computation? In order to show...
Why do we need a formalization of the notion of algorithm or effective computation? In order to show...
Why do we need a formalization of the notion of algorithm or effective computation? In order to show...
The goal of this chapter is to bring to the attention of philosophers of mathematics the concept of ...
During the last four years research on the lower level computational complexity has yielded a rich s...
We provide a new proof of the fact that Mathematical Programming is Turing-complete, and show how it...
We provide a new proof of the fact that Mathematical Programming is Turing-complete, and show how it...
We provide a new proof of the fact that Mathematical Programming is Turing-complete, and show how it...
Information theory is a branch of mathematics that attempts to quantify information. To quantify inf...
Investigating Logics for Feasible Computation The most celebrated open problem in theoretical comput...
In recent years, classical computability has expanded beyond its original scope to address issues re...