DEDUCTIVE OR INDUCTIVE? PROSPECTIVE TEACHERS’ PREFERENCE OF PROOF METHOD ON AN INTERMEDIATE PROOF TASK

Inductive Proof of the Simplex Method

Inductive Proof Method for Computational Secrecy

We investigate inductive methods for proving secrecy properties of network protocols, in a “computational” setting applying a probabilistic polynomial-time adversary. As in cryptographic studies, our secrecy properties assert that no probabilistic polynomial-time distinguisher can win a suitable game presented by a challenger. Our method for establishing secrecy properties uses inductive proofs...

An Inductive Proof Method for Simulation-based Compiler Correctness

We study induction on the program structure as a proof method for bisimulation-based compiler correctness. We consider a first-order language with mutually recursive function definitions, system calls, and an environment semantics. The proof method relies on a generalization of compatibility of function definition with the bisimulation. We use the inductive method to show correctness of a form ...

An Inductive Proof of Hex Uniqueness

A short, inductive proof is presented of the fact that a Hex board cannot be colored such that winning conditions are satisfied for both players. It is well known that the game of Hex, independently invented by Piet Hein and John Nash, always has a winner. In it, two players, Black and White, attempt to connect opposite sides—East and West or North and South—of a parallelogram tiled with hexago...

Towards Intelligent Inductive Proof Engineering

This paper deals with inductive theorem proving (ITP for short). It does not provide new theoretical results but analyses existing ITP methods from an AI point of view. The presentation is based on the implicit ITP approach, i.e. ITP using the well-developed framework of rewriting and completion techniques for systems of equations and rewrite rules. We think that the relevant practical problems...