From a HDL Description to Formal Proof Systems: Principles and Mechanization **Work supported by the EEC under CHARME ESPRIT 3216 BRA

1991 ◽  
pp. 21-41 ◽  
Author(s):  
Laurence PIERRE
Keyword(s):  
Formal Proof ◽  
Proof Systems

Complexity of translations from resolution to sequent calculus

2019 ◽  
Vol 29 (8) ◽  
pp. 1061-1091
Author(s):  
GISELLE REIS ◽  
BRUNO WOLTZENLOGEL PALEO
Keyword(s):  
Automated Reasoning ◽  
Theoretical Basis ◽  
Automated Theorem Proving ◽  
Proof Theory ◽  
Sequent Calculus ◽  
Formal Proof ◽  
Human Beings ◽  
Proof Systems ◽  
Translation Methods ◽  
Resolution Calculus

Resolution and sequent calculus are two well-known formal proof systems. Their differences make them suitable for distinct tasks. Resolution and its variants are very efficient for automated reasoning and are in fact the theoretical basis of many theorem provers. However, being intentionally machine oriented, the resolution calculus is not as natural for human beings and the input problem needs to be pre-processed to clause normal form. Sequent calculus, on the other hand, is a modular formalism that is useful for analysing meta-properties of various logics and is, therefore, popular among proof theorists. The input problem does not need to be pre-processed, and proofs are more detailed. However, proofs also tend to be larger and more verbose. When the worlds of proof theory and automated theorem proving meet, translations between resolution and sequent calculus are often necessary. In this paper, we compare three translation methods and analyse their complexity.

A PARAMETRIC, RESOURCE-BOUNDED GENERALIZATION OF LÖB’S THEOREM, AND A ROBUST COOPERATION CRITERION FOR OPEN-SOURCE GAME THEORY

2019 ◽  
Vol 84 (4) ◽  
pp. 1368-1381
Author(s):  
ANDREW CRITCH
Keyword(s):  
Game Theory ◽  
Formal Verification ◽  
Nash Equilibria ◽  
Source Code ◽  
Formal Proof ◽  
Proof Systems ◽  
Cooperative Program ◽  
Correlated Equilibria ◽  
Computational Resources ◽  
Program Equilibrium

AbstractThis article presents two theorems: (1) a generalization of Löb’s Theorem that applies to formal proof systems operating with bounded computational resources, such as formal verification software or theorem provers, and (2) a theorem on the robust cooperation of agents that employ proofs about one another’s source code as unexploitable criteria for cooperation. The latter illustrates a capacity for outperforming classical Nash equilibria and correlated equilibria, attaining mutually cooperative program equilibrium in the Prisoner’s Dilemma while remaining unexploitable, i.e., sometimes achieving the outcome (Cooperate, Cooperate), and never receiving the outcome (Cooperate, Defect) as player 1.

Incompleteness of a formal system for infinitary finite-quantifier formulas

1971 ◽  
Vol 36 (3) ◽  
pp. 445-455 ◽  
Author(s):  
John Gregory
Keyword(s):  
Formal System ◽  
Formal Proof ◽  
Predicate Calculus ◽  
Proof System ◽  
Proof Systems

In [1], various formal proof systems for infinitary formulas were defined. The formal proof system is the result of extending the basic predicate calculus by adding a collection Σ of axiom schemes and a collection Ω of rules of inference. Let Taut be the collection of all infinitary prepositional tautologies, considered as axiom schemes. Let ΩI consist of all the quantificational rules of independent choices. We will show, in §2 (see Theorem 2.1), that (Taut; 0) is not complete for L∞ω (i.e., infinitary finite-quantifier) sentences; that is, we will exhibit an L∞ω sentence ϕ such that ¬ϕ is true in all models, but ¬ϕ is not provable in (Taut; 0). (The unprovability is shown by a weak forcing version of Boolean general models.) This answers a question of Karp in [1,12.1(i)]. In §4, we will show that our ϕ is “ complete for L∞ω ) sentences.”

Type Theory and Formal Proof

2009 ◽  
Author(s):  
Rob Nederpelt ◽  
Herman Geuvers
Keyword(s):  
Type Theory ◽  
Formal Proof

Secure Cloud Quantum Computing with Verification Based on Quantum Interactive Proof

Impact ◽  
2019 ◽  
Vol 2019 (10) ◽  
pp. 30-32
Author(s):  
Tomoyuki Morimae
Keyword(s):  
Quantum Computing ◽  
Quantum Information ◽  
Theoretical Physics ◽  
View Point ◽  
Research Subjects ◽  
Interactive Proof ◽  
Open Problems ◽  
Main Research ◽  
Proof Systems ◽  
Information Group

In cloud quantum computing, a classical client delegate quantum computing to a remote quantum server. An important property of cloud quantum computing is the verifiability: the client can check the integrity of the server. Whether such a classical verification of quantum computing is possible or not is one of the most important open problems in quantum computing. We tackle this problem from the view point of quantum interactive proof systems. Dr Tomoyuki Morimae is part of the Quantum Information Group at the Yukawa Institute for Theoretical Physics at Kyoto University, Japan. He leads a team which is concerned with two main research subjects: quantum supremacy and the verification of quantum computing.

scholarly journals Better state pictures facilitating state machine characteristic conjecture

2021 ◽  
Author(s):  
Dang Duy Bui ◽  
Kazuhiro Ogata
Keyword(s):  
Virtual Machines ◽  
Mutual Exclusion ◽  
State Machine ◽  
Formal Proof ◽  
The State ◽  
Lessons Learned ◽  
Java Virtual Machines ◽  
Core Part ◽  
Proximity Principle

AbstractThe mutual exclusion protocol invented by Mellor-Crummey and Scott (called MCS protocol) is used to exemplify that state picture designs based on which the state machine graphical animation (SMGA) tool produces graphical animations should be better visualized. Variants of MCS protocol have been used in Java virtual machines and therefore the 2006 Edsger W. Dijkstra Prize in Distributed Computing went to their paper on MCS protocol. The new state picture design of a state machine formalizing MCS protocol is assessed based on Gestalt principles, more specifically proximity principle and similarity principle. We report on a core part of a formal verification case study in which the new state picture design and the SMGA tool largely contributed to the successful completion of the formal proof that MCS protocol enjoys the mutual exclusion property. The lessons learned acquired through our experiments are summarized as two groups of tips. The first group is some new tips on how to make state picture designs. The second one is some tips on how to conjecture state machine characteristics by using the SMGA tool. We also report on one more case study in which the state picture design has been made for the mutual exclusion protocol invented by Anderson (called Anderson protocol) and some characteristics of the protocol have been discovered based on the tips.

Disjoint NP-Pairs and Propositional Proof Systems

2014 ◽  
Vol 45 (4) ◽  
pp. 59-75 ◽  
Author(s):  
C. Glaßer ◽  
A. Hughes ◽  
A. L. Selman ◽  
N. Wisiol
Keyword(s):  
Proof Systems ◽  
Propositional Proof Systems ◽  
Propositional Proof
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