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Finding Proofs and Checking Proofs
, 1996
"... . The classic dichotomy between proof discovery and proof presentation resurfacesin automated deduction. TheLCF style of theorem proving offers a promising way to integrate formal deductive proof with higherlevel algorithmic or heuristic forms of mathematical activity. One way of dealing with the p ..."
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with the potential inefficiency of a reduction to a formal deductive system is to exploit the separation of proof finding and proof checking. This can be relevant both to the implementation difficulty of computer proof assistants, and the speed with which they run. Exploiting the separation makes it practical to use
Chapter 1 Checking proofs
"... Argumentative practice in mathematics evidently takes a number of shapes. An important part of understanding mathematical argumentation, putting aside its special subject matters (numbers, shapes, spaces, sets, functions, etc.), is that mathematical argument often tends toward formality, and it ofte ..."
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Argumentative practice in mathematics evidently takes a number of shapes. An important part of understanding mathematical argumentation, putting aside its special subject matters (numbers, shapes, spaces, sets, functions, etc.), is that mathematical argument often tends toward formality, and it often has superlative epistemic goals:
The Complexity of Generating and Checking Proofs of Membership
, 1996
"... We consider the following questions: 1. Can one compute satisfying assignments for satisfiable Boolean formulas in polynomial time with parallel queries to NP? 2. Is the unique optimal clique problem (UOCLIQUE) complete for P NP[O(log n)] ? 3. Is the unique satisfiability problem (USAT) NP ha ..."
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Cited by 6 (3 self)
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hard? We define a framework that enables us to study the complexity of generating and checking proofs of membership. We connect the above three questions to the complexity of generating and checking proofs of membership for sets in NP and P NP[O(log n)] . We show that an affirmative answer
A framework for checking proofs naturally
 Journal of Intelligent Information Systems
"... Abstract. We propose a natural framework, called NF, which supports development of formal proofs on a computer. NF is based on a theory of Judgments and Derivations. NF is designed by observing how working mathematical theories are created and developed. Our observation is that the notions of judgm ..."
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Cited by 2 (1 self)
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as derivation games and can be played, namely, can write and check proofs. NF is equipped with a higherorder intuitionistic logic and derivations (proofs) are described following Gentzenâ€™s natural deduction style. NF is part of an interactive computer environment CAL (Computation and Logic) and it is also
Checking Proofs from Linked Tools
, 1996
"... We describe a Cambridge project (now completed) which demonstrated the feasibility of producing independent, verified proof checkers for the HOL theorem proving system. We then briefly overview a joint Cambridge University/Hong Kong Baptist University proof checking project which is about to commenc ..."
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We describe a Cambridge project (now completed) which demonstrated the feasibility of producing independent, verified proof checkers for the HOL theorem proving system. We then briefly overview a joint Cambridge University/Hong Kong Baptist University proof checking project which is about
NF: A Natural Framework for Checking Proofs
, 2005
"... We propose a natural framework, called NF, which supports development of formal proofs on a computer. NF is based on a theory of Judgments and Derivations. NF is designed by observing how working mathematical theories are created and developed. Our observation is that the notions of judgmens and der ..."
The Mondex Challenge: Machine Checked Proofs for an Electronic Purse
, 2006
"... The Mondex case study about the specification and refinement of an electronic purse as defined in [SCJ00] has recently been proposed as a challenge for formal systemsupported verification. This paper reports on the successful verification of the major part of the case study using the KIV specificat ..."
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Cited by 24 (9 self)
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specification and verification system. We demonstrate that even though the handmade proofs were elaborated to an enormous level of detail we still could find small errors in the underlying data refinement theory as well as the formal proofs of the case study. We also provide an alternative formalisation
Model Checking Programs
, 2003
"... The majority of work carried out in the formal methods community throughout the last three decades has (for good reasons) been devoted to special languages designed to make it easier to experiment with mechanized formal methods such as theorem provers, proof checkers and model checkers. In this pape ..."
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Cited by 583 (63 self)
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The majority of work carried out in the formal methods community throughout the last three decades has (for good reasons) been devoted to special languages designed to make it easier to experiment with mechanized formal methods such as theorem provers, proof checkers and model checkers
Probabilistic checking of proofs: a new characterization of NP
 JOURNAL OF THE ACM
, 1998
"... We give a new characterization of NP: the class NP contains exactly those languages L for which membership proofs (a proof that an input x is in L) can be verified probabilistically in polynomial time using logarithmic number of random bits and by reading sublogarithmic number of bits from the proof ..."
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Cited by 437 (27 self)
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We give a new characterization of NP: the class NP contains exactly those languages L for which membership proofs (a proof that an input x is in L) can be verified probabilistically in polynomial time using logarithmic number of random bits and by reading sublogarithmic number of bits from
Results 1  10
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654,702