Alphabeta Math

SAT Tableaux and Quantified-Space Completeness

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1 · Prerequisites
Combinatorics
Computability Theory
Real Analysis
Set Theory
2 · Logical flowchart

3 · Items

Definition

Boolean formulas, CNF, and satisfiability

Definition

Bounded Turing-computation tableaux

Lemma

The tableau formula characterizes accepting computations

Lemma

Tableau formulas have polynomial-size polynomial-time CNF encodings

Theorem

Cook-Levin: SAT is NP-complete

Theorem

3SAT is NP-complete

Definition

Polynomial space and nondeterministic polynomial space

Lemma

A space-bounded machine has exponentially many configurations

Theorem

TQBF is PSPACE-complete

Sources