Abstract:Probable security is an important criteria for analyzing the security of cryptographic protocols. However, writing and verifying proofs by hand are prone to errors. This paper introduces the game-based approach of writing security proofs and its automatic technique. It advocates the automatic security proof approach based on process calculus, and presents the initial game and observati...

We consider the problem of analyzing and proving correct simple closure conversion strategies for a higher-order functional language. We specify the conversions as deductive systems, making use of annotated types to provide constraints which guide the construction of the closures. We exploit the ability of deductive systems to specify concisely complex relationships between source terms and clo...

This paper presents a method of learning to solve design problems by generalizing examples. The technique has been developed in the domain of logic circuit design. It involves the use of domain knowledge to analyze examples and produce generalized circuit designs. The method utilizes proofs of design correctness to guide the process of generalization. Our approach is illustrated by showing it c...

Cut-elimination is the most prominent form of proof transformation in logic. The elimination of cuts in formal proofs corresponds to the removal of intermediate statements (lemmas) in mathematical proofs. Cut-elimination can be applied to mine real mathematical proofs, i.e. for extracting explicit and algorithmic information. The system CERES (cut-elimination by resolution) is based on automate...

1. Full proofs for every statement made in the main body. 2. Additional statements that introduce more details and more techniques for analyzing bi-Lipschitz learning settings. 3. Empirical results from the Machine Translation domain that indicate an underlying geometric structure in human and machine translation maps. The empirical results also show these properties for two " experts " : (1) G...

We present cut-elimination as a method of proof mining, in the sense that hidden mathematical information can be extracted by eliminating lemmas from proofs. We present reductive methods for cutelimination and the method ceres (cut-elimination by resolution). A comparison of ceres with reductive methods is given and it is shown that the asymptotic behavior of ceres is superior to that of reduct...

Cut-elimination is the most prominent form of proof transformation in logic. The elimination of cuts in formal proofs corresponds to the removal of intermediate statements (lemmas) in mathematical proofs. The cut-elimination method CERES (cut-elimination by resolution) works by extracting a set of clauses from a proof with cuts. Any resolution refutation of this set then serves as a skeleton of...

Sequent calculus is widely used for formalizing proofs. However, due to the proliferation of data, understanding the proofs of even simple mathematical arguments soon becomes impossible. Graphical user interfaces help in this matter, but since they normally utilize Gentzen’s original notation, some of the problems persist. In this paper, we introduce a number of criteria for proof visualization...

We call proof mining the process of logically analyzing proofs in mathematics with the aim of obtaining new information. In this survey paper we discuss, by means of examples from mathematics, some of the main techniques used in proof mining. We show that those techniques not only apply to proofs based on classical logic, but also to proofs which involve non-effective principles such as the att...