Modular Proof Systems for Partial Functions with Weak Equality

2004 ◽  
pp. 168-182 ◽  
Author(s):  
Harald Ganzinger ◽  
Viorica Sofronie-Stokkermans ◽  
Uwe Waldmann
Keyword(s):  
Partial Functions ◽  
Proof Systems

scholarly journals Modular proof systems for partial functions with Evans equality

2006 ◽  
Vol 204 (10) ◽  
pp. 1453-1492 ◽  
Author(s):  
Harald Ganzinger ◽  
Viorica Sofronie-Stokkermans ◽  
Uwe Waldmann
Keyword(s):  
Partial Functions ◽  
Proof Systems

Methods and clinical applications in nuclear cardiology: a position statement

2002 ◽  
Vol 41 (01) ◽  
pp. 3-13 ◽  
Author(s):  
M. Schäfers
Keyword(s):  
Nuclear Cardiology ◽  
Clinical Medicine ◽  
Imaging Techniques ◽  
Cost Savings ◽  
Cost Benefit ◽  
Position Statement ◽  
Electron Beam Tomography ◽  
Partial Functions ◽  
Cost Benefit Ratio ◽  
Medicine Today

SummaryNuclear cardiological procedures have paved the way for non-invasive diagnostics of various partial functions of the heart. Many of these functions cannot be visualised for diagnosis by any other method (e. g. innervation). These techniques supplement morphological diagnosis with regard to treatment planning and monitoring. Furthermore, they possess considerable prognostic relevance, an increasingly important issue in clinical medicine today, not least in view of the cost-benefit ratio.Our current understanding shows that effective, targeted nuclear cardiology diagnosis – in particular for high-risk patients – can contribute toward cost savings while improving the quality of diagnostic and therapeutic measures.In the future, nuclear cardiology will have to withstand mounting competition from other imaging techniques (magnetic resonance imaging, electron beam tomography, multislice computed tomography). The continuing development of these methods increasingly enables measurement of functional aspects of the heart. Nuclear radiology methods will probably develop in the direction of molecular imaging.

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.

On the action of the implicative closure operator on the set of partial functions of the multivalued logic

2021 ◽  
Vol 31 (3) ◽  
pp. 155-164
Author(s):  
Sergey S. Marchenkov
Keyword(s):  
Closure Operator ◽  
Multivalued Logic ◽  
Partial Functions ◽  
Logical Implication

Abstract On the set P k ∗ $\begin{array}{} \displaystyle P_k^* \end{array}$ of partial functions of the k-valued logic, we consider the implicative closure operator, which is the extension of the parametric closure operator via the logical implication. It is proved that, for any k ⩾ 2, the number of implicative closed classes in P k ∗ $\begin{array}{} \displaystyle P_k^* \end{array}$ is finite. For any k ⩾ 2, in P k ∗ $\begin{array}{} \displaystyle P_k^* \end{array}$ two series of implicative closed classes are defined. We show that these two series exhaust all implicative precomplete classes. We also identify all 8 atoms of the lattice of implicative closed classes in P 3 ∗ $\begin{array}{} \displaystyle P_3^* \end{array}$ .

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

Complete proof systems for algebraic simply-typed terms

1994 ◽  
Vol VII (3) ◽  
pp. 220-226
Author(s):  
Stavros S. Cosmadakis
Keyword(s):  
Complete Proof ◽  
Proof Systems

A taxonomy of proof systems (part 1)

1993 ◽  
Vol 24 (4) ◽  
pp. 2-13 ◽  
Author(s):  
Oded Goldreich
Keyword(s):  
Proof Systems

scholarly journals Computational and Proof Complexity of Partial String Avoidability

2021 ◽  
Vol 13 (1) ◽  
pp. 1-25
Author(s):  
Dmitry Itsykson ◽  
Alexander Okhotin ◽  
Vsevolod Oparin
Keyword(s):  
Lower Bounds ◽  
Circuit Complexity ◽  
Conjunctive Normal Form ◽  
Proof Complexity ◽  
Proof Systems ◽  
Finite Set ◽  
Propositional Proof Systems ◽  
Classical Proof ◽  
Exponential Size ◽  
Infinite String

The partial string avoidability problem is stated as follows: given a finite set of strings with possible “holes” (wildcard symbols), determine whether there exists a two-sided infinite string containing no substrings from this set, assuming that a hole matches every symbol. The problem is known to be NP-hard and in PSPACE, and this article establishes its PSPACE-completeness. Next, string avoidability over the binary alphabet is interpreted as a version of conjunctive normal form satisfiability problem, where each clause has infinitely many shifted variants. Non-satisfiability of these formulas can be proved using variants of classical propositional proof systems, augmented with derivation rules for shifting proof lines (such as clauses, inequalities, polynomials, etc.). First, it is proved that there is a particular formula that has a short refutation in Resolution with a shift rule but requires classical proofs of exponential size. At the same time, it is shown that exponential lower bounds for classical proof systems can be translated for their shifted versions. Finally, it is shown that superpolynomial lower bounds on the size of shifted proofs would separate NP from PSPACE; a connection to lower bounds on circuit complexity is also established.

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