A Bijective Proof of the ASM Theorem Part II: ASM Enumeration and ASM–DPP Relation

On Gurevich’s Theorem for Sequential ASM

Abstract-State Machines have been introduced as “a computation model that is more powerful and more universal than standard computation models”, by Yuri Gurevich in 1985 ([Gur85]). ASM gained much attention as a specification method, in particular for the description of the semantics of programming languages, communication protocols, distributed algorithms, etc. Gurevich proved recently that a ...

asm . org

A Bijective Proof of Stanley's Shuffling Theorem

For two permutations o and u on disjoint sets of integers, consider forming a permutation on the combined sets by "shuffling" o and u (i.e., a and co appear as subsequences). Stanley [10], by considering P-partitions and a g-analogue of Saalschutz's 3F2 summation, obtained the generating function for shuffles of o and u with a given number of falls (an element larger than its successor) with re...

A Bijective Proof for Reciprocity Theorem

In this paper, we study the graph polynomial that records spanning rooted forests fG of a given graph. This polynomial has a remarkable reciprocity property. We give a new bijective proof for this theorem which has Prüfer coding as a special case.

SMT-Based Automatic Proof of ASM Model Refinement

Model refinement is a technique indispensable for modeling large and complex systems. Many formal specification methods share this concept which usually comes together with the definition of refinement correctness, i.e., the mathematical proof of a logical relation between an abstract model and its refined models. Model refinement is one of the main concepts which the Abstract State Machine (AS...