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Robust Computer Algebra, Theorem Proving, and Oracle AI [article]

Gopal P. Sarma, Nick J. Hay
2017 arXiv   pre-print
On the other hand, we identify computer algebra systems (CASs) as being primitive examples of domain-specific oracles for mathematics and argue that efforts to integrate computer algebra systems with theorem  ...  We review approaches to interfacing CASs with theorem provers, describe well-defined architectural deficiencies that have been identified with CASs, and suggest possible lines of research and practical  ...  We would also like to thank the guest editors of Informatica, Ryan Carey, Matthijs Maas, Nell Watson, and Roman Yampolskiy, for organizing this special issue.  ... 
arXiv:1708.02553v2 fatcat:hesasayvljb3vmjqsw7sniutdm

Robust Computer Algebra, Theorem Proving, and Oracle AI

Gopal P. Sarma, Nick J. Hay
2017 Social Science Research Network  
On the other hand, we identify computer algebra systems (CASs) as being primitive examples of domain-specific oracles for mathematics and argue that efforts to integrate computer algebra systems with theorem  ...  We review approaches to interfacing CASs with theorem provers, describe well-defined architectural deficiencies that have been identified with CASs, and suggest possible lines of research and practical  ...  We would also like to thank the guest editors of Informatica, Ryan Carey, Matthijs Maas, Nell Watson, and Roman Yampolskiy, for organizing this special issue.  ... 
doi:10.2139/ssrn.3038545 fatcat:w3bzqxgopbdwtbqvsckcsfdjoq

The Effect of the Theorem Prover in Cognitive Science [chapter]

Tadashi Takahashi, Hidetsune Kobayashi
2006 Lecture Notes in Computer Science  
Strategies are used as knowledge to plan solutions and decide procedures. A computer algebra system with a theorem prover is being developed.  ...  We must consider the theorem prover from not only the perspective of its effect on cognitive science, but also from the perspective of mathematical studies.  ...  The system combines methods of automated theorem proving and also integrates programming in a natural way.  ... 
doi:10.1007/11758501_139 fatcat:wxav67tdfncx5a6ws7myi7vh2m

Automated Theorem Proving In Support Of Computer Algebra: Symbolic Definite Integration As A Case Study [chapter]

A.A. Adams, H. Gottliebsen, S.A. Linton, U. Martin
1999 Zenodo  
cases where computer algebra systems [CAS] do not.  ...  parameters and side conditions, against an entry in a verifiable table and uses a call to a library of lemmas about the reals in the theorem prover PVS to aid in the transformation of the table entry  ...  for advice on computer algebra, and Bruno Dutertre for allowing us to extend his code for the reals in PVS.  ... 
doi:10.5281/zenodo.810861 fatcat:5jn2aedwibd4jczs2hzhx3uwrm

TYPELAB: An environment for modular program development [chapter]

F. W. von Henke, M. Luther, M. Strecker
1997 Lecture Notes in Computer Science  
Acknowledgments The design of the TYPELAB language and system has to a great extent been influenced by Holger Pfeifer, Harald Ruet3 and Detlef Schwier. Matthias Wagner  ...  implemented most of the Tableaux style theorem prover.  ...  -Theorems give rise to proof obligations, which can be solved using the prover integrated into TYPELAB. Specification types are first-class objects in TYPELAB.  ... 
doi:10.1007/bfb0030645 fatcat:tgvflrdmjfamxld72z52tcybje

Integrating Automated and Interactive Theorem Proving [chapter]

Ahrendt, Beckert, Hähnle, Menzel, Reif, Schellhorn, Schmitt
1998 Applied Logic Series  
Apart from first-order logic theorem proving, the most important reasoning methods being integrated in interactive frameworks are: computer algebra (Harrison and Théry, 1993; Ballarin et al., 1995) ,  ...  With the improvements of the integrated system we have implemented so far, the integrated system is now able to prove 21 (36%) theorems fully automatic.  ... 
doi:10.1007/978-94-017-0435-9_4 fatcat:nsfxar65jbhybcrsdvi2stys6u

Reasoning about coding theory: The benefits we get from computer algebra [chapter]

Clemens Ballarin, Lawrence C. Paulson
1998 Lecture Notes in Computer Science  
The unsoundness of computer algebra systems is a major problem in interfacing them to theorem provers.  ...  of the theorem prover.  ...  This work has been funded in part by the Studienstiftung des deutschen Volkes and by EPSRC grant GR/K57381 "Mechanizing Temporal Reasoning".  ... 
doi:10.1007/bfb0055902 fatcat:3y4foskxojaanofx67uk2ageyi

Formalization and Implementation of Algebraic Methods in Geometry

Filip Marić, Ivan Petrović, Danijela Petrović, Predrag Janičić
2012 Electronic Proceedings in Theoretical Computer Science  
We describe our ongoing project of formalization of algebraic methods for geometry theorem proving (Wu's method and the Groebner bases method), their implementation and integration in educational tools  ...  ., the lack of formal links between algebraic methods and synthetic geometry and the lack of self-contained implementations of algebraic methods suitable for integration with dynamic geometry tools) and  ...  Discover is a system for automated proving and discovery in geometry, based on two computer algebra systems, CoCoA and Mathematica [3] .  ... 
doi:10.4204/eptcs.79.4 fatcat:j7pyqmy6nvbpraduv6tbkhmmt4

Towards a Geometry Automated Provers Competition

Nuno Baeta, Pedro Quaresma, Zoltán Kovács
2020 Electronic Proceedings in Theoretical Computer Science  
The geometry automated theorem proving area distinguishes itself by a large number of specific methods and implementations, different approaches (synthetic, algebraic, semi-synthetic) and different goals  ...  CPU time), the possibility of visual and/or readable proofs is also an expected output against which the geometry automated theorem provers (GATP) should be measured.  ...  Introduction The area of geometry automated theorem proving distinguishes itself by a large number of specific methods and implementations.  ... 
doi:10.4204/eptcs.313.6 fatcat:7qd6linvqnbifeh4lxwe75ii6y

Towards the Mathematics Software Bus

Jacques Calmet, Karsten Homann
1997 Theoretical Computer Science  
Communication and cooperation mechanisms for logical and symbolic computation systems enable to study and solve new classes of problems and to perform efficient computation in mathematics through cooperating  ...  Such an environment will provide combinations of graphics, editing and computation tools through interfaces to already existing powerful software by flexible and powerful semantically integration.  ...  Jackson [15] presents an interaction to provide expressive algebra of constructive type theory in computer algebra. The theorem prover NUPRL is an algebraic oracle to the CAS WEYL.  ... 
doi:10.1016/s0304-3975(97)00066-2 fatcat:xl6sovpvdbgpzohaegycja4edy

Proof-of-work certificates that can be efficiently computed in the cloud [article]

Jean-Guillaume Dumas
2018 arXiv   pre-print
Differently, we will here present problem-specific procedures in computer algebra, e.g. for exact linear algebra computations, that are Prover-optimal, that is that have much less financial overhead.  ...  However, the extra cost of the computations for the Prover (and therefore the extra cost to the customer), although only almost a constant factor of the overall work, is nonetheless prohibitive in practice  ...  systems A proof system usually has two parts, a theorem T and a proof Π, and the validity of the proof can be checked by a verifier V .  ... 
arXiv:1806.11293v2 fatcat:nhkhxiojmzfl3a63fmmk32dthi

Proof-of-Work Certificates that Can Be Efficiently Computed in the Cloud (Invited Talk) [chapter]

Jean-Guillaume Dumas
2018 Lecture Notes in Computer Science  
Differently, we will here present problem-specific procedures in computer algebra, e.g. for exact linear algebra computations, that are Proveroptimal, that is that have much less financial overhead. •  ...  However, the extra cost of the computations for the Prover (and therefore the extra cost to the customer), although only almost a constant factor of the overall work, is nonetheless prohibitive in practice  ...  or integral domains. 2 Interactive protocols, the PCP theorem and homomorphic encryption Arthur-Merlin interactive proof systems A proof system usually has two parts, a theorem T and a proof Π, and  ... 
doi:10.1007/978-3-319-99639-4_1 fatcat:7usrmrmjizg45g2tyfyye3rqwe

Automated deduction: achievements and future directions

D. W. Loveland
2000 Communications of the ACM  
We use the term AD for automated theorem provers, counterexample (model) generation, and consequence generators, in both fully automated and interactive systems.  ...  AD has spawned useful tools and systems, and offers great promise for making substantial progress on some of the most challenging problems in computer science and engineering--such as how to improve the  ...  Most computer algebra systems currently are unsound, and integration cannot be done without modification.  ... 
doi:10.1145/352515.352529 fatcat:iv3ooanjpjazvmytbmlziih2si

Experiments with an Agent-Oriented Reasoning System [chapter]

Christoph Benzmüller, Manfred Kerber, Mateja Jamnik, Volker Sorge
2001 Lecture Notes in Computer Science  
It particularly supports cooperative proofs between reasoning systems which are strong in different application areas, e.g., higher-order and first-order theorem provers and computer algebra systems.  ...  The approach combines ideas from two subfields of AI (theorem proving/proof planning and multi-agent systems) and makes use of state of the art distribution techniques to decentralise and spread its reasoning  ...  This work was supported by EPSRC grants GR/M99644 and GR/M22031 (Birmingham), and the SFB 378 (Saarbrücken).  ... 
doi:10.1007/3-540-45422-5_29 fatcat:6twdpntxvbexxl5g7l5uc7tqru

CSP-CASL-Prover: A Generic Tool for Process and Data Refinement

Liam O'Reilly, Markus Roggenbach, Yoshinao Isobe
2009 Electronical Notes in Theoretical Computer Science  
The main issue in integrating the tools Hets and Csp-Prover into a Csp-Casl-Prover is to implement -in Isabelle/HOL -Csp-Casl's construction of an alphabet of communications out of an algebraic specification  ...  In our paper, we describe how a combination of the existing tools Hets and Csp-Prover can solve the challenges that Csp-Casl raises on integrated theorem proving for processes and data.  ...  Catesbeiana (jr) for his valuable insights into the very nature of electronic payment systems.  ... 
doi:10.1016/j.entcs.2009.08.018 fatcat:thw7awi56nandeb4wfoaljwr4i
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