Cut normal forms and proof complexity

On the Proof Complexity of Cut-Free Bounded Deep Inference

It has recently been shown that cut-free deep inference systems exhibit an exponential speed-up over cut-free sequent systems, in terms of proof size. While this is good for proof complexity, there remains the problem of typically high proof search non-determinism induced by the deep inference methodology: the higher the depth of inference, the higher the non-determinism. In this work we improv...

Proof Complexity of the Cut-free Calculus of Structures

We investigate the proof complexity of analytic subsystems of the deep inference proof system SKSg (the calculus of structures). Exploiting the fact that the cut rule (i↑) of SKSg corresponds to the ¬-left rule in the sequent calculus, we establish that the “analytic” system KSg+c↑ has essentially the same complexity as the monotone Gentzen calculus MLK . In particular, KSg + c↑ quasipolynomial...

Constructive Derivation and Proof of Quadratic Normal Forms

Abstract The normal forms for linearly controllable quadratic system are derived and proved for single-input continuous system, single-input discrete sytem and multi-input continuous system in a constructive way.

Proof Fragments, Cut-Elimination and Cut-Introduction

Cut-elimination is usually presented as a set of local proof reduction steps together with a terminating strategy thus showing the existence of cut-free proofs for all provable sequents. Viewing cut-elimination as a transformation of mathematical proofs, not only the existence but also the structure and content of the cut-free proofs deserves investigation. In this paper we use proof skeletons ...

Boundary NLC Graph Grammars-Basic Definitions, Normal Forms, and Complexity