Complexity arguments in algebraic language theory

Priority Arguments in Complexity Theory

machine-independent) complexity theory is basically a theory which establishes limits on what may be said about the complexity of specific recursive functions. (For example, the speed-up theorem [1] shows that it is not always possible to discover close upper and lower bounds for the complexity of a function.) As such, its basic proof method is diagonalization. Sacks, Spector, etc. [2], [3] hav...

Priority Arguments in Computability Theory, Model Theory, and Complexity Theory

These notes present various priority arguments in classical computability theory, effective model theory, and complexity theory in a uniform style. Our notation usually follows Soare (1986) with some exceptions. We view Turing functionals as c.e. sets Φ of triples ⟨x, y, σ⟩, denoting that Φ(σ;x) ↓= y. (Of course, we have to impose the obvious compatibility condition, namely, that if ⟨x, y, σ⟩, ...

Algebraic Complexity Theory

Algebraic Complexity Theory

Algebraic complexity theory investigates the computational cost of solving problems with an algebraic flavor. Several cost measures are of interest. We consider arithmetic circuits, which can perform the (exact) arithmetic operations +, -, *, / at unit cost, and take their size ( = sequential time) or their depth (=parallel time) as cost functions. This is a natural "structured" model of comput...

Independence in Algebraic Complexity Theory