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A Generic Cyclic Theorem Prover [chapter]

James Brotherston, Nikos Gorogiannis, Rasmus L. Petersen
2012 Lecture Notes in Computer Science  
We describe the design and implementation of an automated theorem prover realising a fully general notion of cyclic proof.  ...  Cyclist is based on a new, generic theory of cyclic proofs that can be instantiated to a wide variety of logics.  ...  In this paper we describe the design and implementation of a new cyclic theorem prover, called Cyclist, based on a generic theory of cyclic proofs and instantiable to a wide variety of logical systems.  ... 
doi:10.1007/978-3-642-35182-2_25 fatcat:wxs6473vzvcsnpeccc66unyim4

Automated generation of readable proofs with geometric invariants

Shang-Ching Chou, Xiao-Shan Gao, Jing-Zhong Zhang
1996 Journal of automated reasoning  
The prover based on the full-angle method has been used to produce short and elegant proofs for more than one hundred difficult geometry theorems.  ...  We present a set of rules based on full-angles as the basis of automated geometry theorem proving. We extend the idea of eliminating variables and points to the idea of eliminating lines.  ...  However, for the general-purpose geometry theorem provers based on the algebraic methods, the proofs require exceedingly large amount of computer memory which are currently not available on most computer  ... 
doi:10.1007/bf00283134 fatcat:wt4ur5rvkbbzhfys7q24r5ljqi

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

Clemens Ballarin, Lawrence C. Paulson
1998 Lecture Notes in Computer Science  
of the theorem prover.  ...  The unsoundness of computer algebra systems is a major problem in interfacing them to theorem provers.  ...  Isabelle Isabelle is a natural deduction-style theorem prover.  ... 
doi:10.1007/bfb0055902 fatcat:3y4foskxojaanofx67uk2ageyi

A System for Computing and Reasoning in Algebraic Topology [chapter]

Jónathan Heras, Vico Pascual, Julio Rubio
2011 Lecture Notes in Computer Science  
The fKenzo system provides a friendly graphical user interface which allows the user to interact with both the Kenzo and GAP Computer Algebra systems and, also, with the ACL2 Theorem Prover by means of  ...  In this paper we present the fKenzo system, an integral assistant for teaching and research in (a subset of) Algebraic Topology.  ...  From the theorem proving side, ACL2 [7] , a first order logic theorem prover tool, is the core for verifying the correctness of statements.  ... 
doi:10.1007/978-3-642-22673-1_26 fatcat:j3fe7fkfajfgzcfdn5czfanqyi

Automated Cyclic Entailment Proofs in Separation Logic [chapter]

James Brotherston, Dino Distefano, Rasmus Lerchedahl Petersen
2011 Lecture Notes in Computer Science  
Our procedure has been implemented via a deep embedding of cyclic proofs in the HOL Light theorem prover.  ...  We present a general automated proof procedure, based upon cyclic proof, for inductive entailments in separation logic.  ...  Here we have focused on developing a general cyclic entailment checker which could eventually become an off-the-shelf prover for verification tools or theorem provers.  ... 
doi:10.1007/978-3-642-22438-6_12 fatcat:k7uyydhxkzaw5myz5paw67yfli

Search methods revisited [chapter]

Gao Xiao-Shan
2000 Mathematics Mechanization and Applications  
We also discuss several key issues in developing an efficient geometry theorem prover with heuristic search methods.  ...  which shows surprising power in terms of proving and discovering difficult geometry theorems.  ...  [HF, HC] = [EF, EC] :-(9)cyclic[CF EH]. 8. cyclic[AF BE] :-(hyp)perp[F B, F A], (hyp)perp[EB, EA]. 9. cyclic[CF EH] :-(hyp)perp[F H, F C], (hyp)perp[EH, EC]. Example 10.3: The Five Circle Theorem  ... 
doi:10.1016/b978-012734760-8/50011-9 fatcat:7jnnwy3q5jfj7a7umhlfl7s55i

Automated generation of readable proofs with geometric invariants

Shang-Ching Chou, Xiao-Shan Gao, Jing-Zhong Zhang
1996 Journal of automated reasoning  
in geometry, especially to produce multiple and shortest proofs of a given geometry theorem.  ...  Control and search strategies are proposed and experimented with to enhance the efficiency of the prover.  ...  (L11)) (S ECA = EC·EA·CA 2δ , because cyclic(E,C,A).  ... 
doi:10.1007/bf00283133 fatcat:3l6va4a4cvdb3oa226wto6wwje

Batch Verification for Equality of Discrete Logarithms and Threshold Decryptions [chapter]

Riza Aditya, Kun Peng, Colin Boyd, Ed Dawson, Byoungcheon Lee
2004 Lecture Notes in Computer Science  
A general technique of batch verification for equality of discrete logarithms is proposed.  ...  Our technique offers large computational savings when employed in schemes with a large number of ciphertexts to be decrypted, such as in e-voting or e-auction schemes using threshold decryption.  ...  Theorem 1. For j ∈ {1, . . . , m}, G is a cyclic group with q as the smallest factor of ord (G), generators g and c j , and a security parameter l, where 2 l < q.  ... 
doi:10.1007/978-3-540-24852-1_36 fatcat:46mbmsgmurfmbcaol67qthkdym

Coming to Terms with Quantified Reasoning [article]

Laura Kovacs, Simon Robillard, Andrei Voronkov
2016 arXiv   pre-print
We implemented our work in the first-order theorem prover Vampire and evaluated it on a large number of algebraic data type benchmarks, as well as game theory constraints.  ...  Our first method is a conservative extension of the theory of term algebras using a finite number of statements, while our second method relies on extending the superposition calculus of first-order theorem  ...  More generally, our work makes an important step towards closing the gap between SMT solvers and first-order theorem provers.  ... 
arXiv:1611.02908v1 fatcat:gfxm4sj7prgcrdpl3ymffnhp4m

An identification system based on the explicit isomorphism problem [article]

Sándor Z. Kiss, Péter Kutas
2021 arXiv   pre-print
We design a statistical zero knowledge protocol which relies on the hardness of computing isomorphisms between orders in division algebras which generalizes a protocol by Hartung and Schnorr, which relies  ...  We propose a new identification system based on algorithmic problems related to computing isomorphisms between central simple algebras.  ...  The Integer Order Isomorphism Problem is to find an Theorem 4. ( [26] , p.278) Let L be a cyclic extension of K and let a ∈ K \ {0}.  ... 
arXiv:1812.09130v3 fatcat:m7we5nsxtzbjzfdzua26xfm5pm

Coming to terms with quantified reasoning

Laura Kovács, Simon Robillard, Andrei Voronkov
2017 Proceedings of the 44th ACM SIGPLAN Symposium on Principles of Programming Languages - POPL 2017  
We implemented our work in the first-order theorem prover Vampire and evaluated it on a large number of algebraic data type benchmarks, as well as game theory constraints.  ...  Our first method is a conservative extension of the theory of term algebras using a finite number of statements, while our second method relies on extending the superposition calculus of first-order theorem  ...  More generally, our work makes an important step towards closing the gap between SMT solvers and first-order theorem provers.  ... 
doi:10.1145/3009837.3009887 fatcat:26soclwzs5gkbkc5ao2t42vg7m

Abstract notions and inference systems for proofs by mathematical induction [chapter]

Claus-Peter Wirth, Klaus Becker
1995 Lecture Notes in Computer Science  
To overcome these problems we propose to develop soundness proofs systematically by presenting an abstract frame inference system a priori and then to design each concrete inference rule locally as a sub-rule  ...  of some frame inference rule and to show its soundness by a small local proof establishing this sub-rule relationship.  ...  To succeed in proving an inductive theorem in finite time, implicit inductive theorem provers have to solve exactly the same problem as explicit inductive theorem provers, namely to find a finite cyclic  ... 
doi:10.1007/3-540-60381-6_21 fatcat:wov5m7zlnrhrbpkovky2ezr6sm

Local Checkability in Dynamic Networks

Klaus-Tycho Foerster, Oliver Richter, Jochen Seidel, Roger Wattenhofer
2017 Proceedings of the 18th International Conference on Distributed Computing and Networking - ICDCN '17  
In such a PVP, a prover P assigns a label to each vertex of an initial graph Gi.  ...  Furthermore, we show that no PVP can be found for s-t-reachability nor general cyclicity that can consider multiple inconsistencies.  ...  A simple coding of these vertex classes generates the labeling the prover can put on the graph Gi ∈ Y .  ... 
doi:10.1145/3007748.3007779 fatcat:5f6wj2lrhjgz5nqlarzphbrory

Generating Counterexamples for Structural Inductions by Exploiting Nonstandard Models [chapter]

Jasmin Christian Blanchette, Koen Claessen
2010 Lecture Notes in Computer Science  
Repair the property's statement or its underlying specification so that it becomes a theorem. 2. Generalize the property and/or prove auxiliary properties. 3. Work harder on a proof.  ...  The property is not a theorem. 2. The property is a theorem but is too weak to support the induction step. 3. The property is a theorem and is inductive, although no proof has been found yet.  ...  Background Isabelle/HOL Isabelle [13] is a generic theorem prover whose built-in metalogic is an intuitionistic fragment of higher-order logic [7, 9] .  ... 
doi:10.1007/978-3-642-16242-8_10 fatcat:z3ya4wwljbarbaqnyl5owxeimu

Interactive Proofs with Polynomial-Time Quantum Prover for Computing the Order of Solvable Groups

François Le Gall, Tomoyuki Morimae, Harumichi Nishimura, Yuki Takeuchi, Michael Wagner
2018 International Symposium on Mathematical Foundations of Computer Science  
Our result shows that computing the order of a solvable group, which is one of the most general problems for which quantum computing exhibits an exponential speed-up with respect to classical computing  ...  In this paper we consider what can be computed by a user interacting with a potentially malicious server, when the server performs polynomial-time quantum computation but the user can only perform polynomial-time  ...  If the prover learns that this element is in H i−1 then the prover applies Algorithm A 1 of Theorem 5 to obtain a decomposition (a i,1 , . . . , a i,i−1 ) of h i over H i−1 , and sends to the verifier  ... 
doi:10.4230/lipics.mfcs.2018.26 dblp:conf/mfcs/GallMNT18 fatcat:svboagyj3rgarmbwesygc4c6eu
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