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A Generic Cyclic Theorem Prover
[chapter]

2012
*
Lecture Notes in Computer Science
*

We describe the design and implementation of an automated

doi:10.1007/978-3-642-35182-2_25
fatcat:wxs6473vzvcsnpeccc66unyim4
*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. ...##
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Automated generation of readable proofs with geometric invariants

1996
*
Journal of automated reasoning
*

The

doi:10.1007/bf00283134
fatcat:wt4ur5rvkbbzhfys7q24r5ljqi
*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 ...##
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Reasoning about coding theory: The benefits we get from computer algebra
[chapter]

1998
*
Lecture Notes in Computer Science
*

of the

doi:10.1007/bfb0055902
fatcat:3y4foskxojaanofx67uk2ageyi
*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*. ...##
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A System for Computing and Reasoning in Algebraic Topology
[chapter]

2011
*
Lecture Notes in Computer Science
*

The fKenzo system provides

doi:10.1007/978-3-642-22673-1_26
fatcat:j3fe7fkfajfgzcfdn5czfanqyi
*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. ...##
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Automated Cyclic Entailment Proofs in Separation Logic
[chapter]

2011
*
Lecture Notes in Computer Science
*

Our procedure has been implemented via

doi:10.1007/978-3-642-22438-6_12
fatcat:k7uyydhxkzaw5myz5paw67yfli
*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*. ...##
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Search methods revisited
[chapter]

2000
*
Mathematics Mechanization and Applications
*

We also discuss several key issues in developing an efficient geometry

doi:10.1016/b978-012734760-8/50011-9
fatcat:7jnnwy3q5jfj7a7umhlfl7s55i
*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*...##
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Automated generation of readable proofs with geometric invariants

1996
*
Journal of automated reasoning
*

in geometry, especially to produce multiple and shortest proofs of

doi:10.1007/bf00283133
fatcat:3l6va4a4cvdb3oa226wto6wwje
*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*). ...##
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Batch Verification for Equality of Discrete Logarithms and Threshold Decryptions
[chapter]

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. ...

##
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Coming to Terms with Quantified Reasoning
[article]

2016
*
arXiv
*
pre-print

We implemented our work in the first-order

arXiv:1611.02908v1
fatcat:gfxm4sj7prgcrdpl3ymffnhp4m
*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*. ...##
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An identification system based on the explicit isomorphism problem
[article]

2021
*
arXiv
*
pre-print

We design

arXiv:1812.09130v3
fatcat:m7we5nsxtzbjzfdzua26xfm5pm
*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}. ...##
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Coming to terms with quantified reasoning

2017
*
Proceedings of the 44th ACM SIGPLAN Symposium on Principles of Programming Languages - POPL 2017
*

We implemented our work in the first-order

doi:10.1145/3009837.3009887
fatcat:26soclwzs5gkbkc5ao2t42vg7m
*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*. ...##
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Abstract notions and inference systems for proofs by mathematical induction
[chapter]

1995
*
Lecture Notes in Computer Science
*

To overcome these problems we propose to develop soundness proofs systematically by presenting an abstract frame inference system

doi:10.1007/3-540-60381-6_21
fatcat:wov5m7zlnrhrbpkovky2ezr6sm
*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*...##
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Local Checkability in Dynamic Networks

2017
*
Proceedings of the 18th International Conference on Distributed Computing and Networking - ICDCN '17
*

In such

doi:10.1145/3007748.3007779
fatcat:5f6wj2lrhjgz5nqlarzphbrory
*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 . ...##
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Generating Counterexamples for Structural Inductions by Exploiting Nonstandard Models
[chapter]

2010
*
Lecture Notes in Computer Science
*

Repair the property's statement or its underlying specification so that it becomes

doi:10.1007/978-3-642-16242-8_10
fatcat:z3ya4wwljbarbaqnyl5owxeimu
*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] . ...##
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Interactive Proofs with Polynomial-Time Quantum Prover for Computing the Order of Solvable Groups

2018
*
International Symposium on Mathematical Foundations of Computer Science
*

Our result shows that computing the order of

doi:10.4230/lipics.mfcs.2018.26
dblp:conf/mfcs/GallMNT18
fatcat:svboagyj3rgarmbwesygc4c6eu
*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 ...
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