Using Automated Theorem Provers in Nonassociative Algebra
نویسندگان
چکیده
We present a case study on how mathematicians use automated theorem provers to solve open problems in (non-associative) algebra.
منابع مشابه
First-Order Theorem Prover Evaluation w.r.t. Relation- and Kleene Algebra
Recently it has been shown that off-the-shelf first-order automated theorem provers can successfully verify statements of substantial complexity in relation and Kleene algebras. Until now most of our proof automation had been done using McCune’s theorem prover Prover9, while others like SPASS and Vampire were not used extensively. In this paper we use more than 500 theorems to compare and evalu...
متن کاملSpecification and Integration of Theorem Provers and Computer Algebra Systems
Computer algebra systems (CASs) and automated theorem provers (ATPs) exhibit complementary abilities. CASs focus on efficiently solving domain-specific problems. ATPs are designed to allow for the formalization and solution of wide classes of problems within some logical framework. Integrating CASs and ATPs allows for the solution of problems of a higher complexity than those confronted by each...
متن کاملTool-Based Verification of a Relational Vertex Coloring Program
We present different approaches of using a special purpose computer algebra system and theorem provers in software verification. To this end, we first develop a purely algebraic while-program for computing a vertex coloring of an undirected (loop-free) graph. For showing its correctness, we then combine the well-known assertion-based verification method with relation-algebraic calculations. Bas...
متن کاملCombining Automated Theorem Provers and Computer Algebra Systems for Generating Formal Proofs of Complexity Bounds
Over the past few years, the traditional separation between automated theorem provers and computer algebra systems has slowly been eroded as both sides venture into foreign territory. But despite recent progress, theorem provers still have difficulties with basic arithmetic while computer algebra system inherently produce “untrusted” results that are not easily verified. We were able to combine...
متن کاملEmploying Theory Formation to Guide Proof Planning
The invention of suitable concepts to characterise mathematical structures is one of the most challenging tasks for both human mathematicians and automated theorem provers alike. We present an approach where automatic concept formation is used to guide non-isomorphism proofs in the residue class domain. The main idea behind the proof is to automatically identify discriminants for two given stru...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008