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About 10,000 papers for “Complexity class”

The Complexity Of Class Polyl

Vega, Frank · Zenodo (CERN European Organization for Nuclear Research) · 2018

We define the class polyL as the set of languages that can be decided in deterministic polylogarithmic space. We prove every language in NP is in polyL. In this way, we show every language in P is in polyL. Moreover, since every language in polyL is in QP, then every problem in NP can be decided in a quasi-polynomial time.

Cited by 0Open access

Reduced complexity SIMD-class architectures

Michael A. Glover, Andrzej Ruciński, Wallace T. Miller · 2002

System engineering applied in leading microelectronic technologies requires novel computing architectures. These architectural counterparts of emerging technologies are expected to be dramatically different from existing architectural paradigms. To address this need, we are introducing a class of architectures which maintain computing robustness and reduced complexity in the interconnect domain, and still substantially differ from well established systolic systems. A class representative, a DRAM based system, is described in detail, with a permutation generation as an example of application.

Cited by 0

Metrics suite for class complexity

John Michura, Miriam A. M. Capretz · 2005

Though software engineering seems to focus on the development of software, most of the funds are spent maintaining and testing the systems. The ability to predict effort required to test and maintain is valuable to an organization interested in allocating project resources accordingly. This paper reviews the metrics cyclomatic complexity and weighted methods per class. The flaws in weighted methods per class are examined and a suite of metrics to determine and justify class complexity is proposed. This paper also discusses the design of a software tool that can be used to extract the values for the proposed metrics suite. The benefits of the software tool are also discussed.

Cited by 19

The complexity of class TAUTOLOGY-NP

Vega, Frank · Figshare · 2018

P versus NP is considered as one of the most important open problems in computer science. This consists in knowing the answer of the following question: Is P equal to NP? This question was first mentioned in a letter written by John Nash to the National Security Agency in 1955. A precise statement of the P versus NP problem was introduced independently in 1971 by Stephen Cook and Leonid Levin. Since that date, all efforts to find a proof for this problem have failed. TAUTOLOGY-L is a problem of deciding given an instance x of a language L whether every possible appropriate answer for x is actually a solution in L. The class TAUTOLOGY-NP contains those languages TAUTOLOGY-L where L is in NP. Another major complexity class is NP-complete. To attack the P versus NP question the concept of NP-completeness has been very useful. We define the completeness of TAUTOLOGY-NP using the polynomial time reduction as well. We demonstrate there is a TAUTOLOGY-L language that is not only complete for TAUTOLOGY-NP, but it is also in P.

Cited by 0Open access

The complexity of class TAUTOLOGY-NP

Vega, Frank · Figshare · 2018

P versus NP is considered as one of the most important open problems in computer science. This consists in knowing the answer of the following question: Is P equal to NP? This question was first mentioned in a letter written by John Nash to the National Security Agency in 1955. A precise statement of the P versus NP problem was introduced independently in 1971 by Stephen Cook and Leonid Levin. Since that date, all efforts to find a proof for this problem have failed. TAUTOLOGY-L is a problem of deciding given an instance x of a language L whether every possible appropriate answer for x is actually a solution in L. The class TAUTOLOGY-NP contains those languages TAUTOLOGY-L where L is in NP. Another major complexity class is NP-complete. To attack the P versus NP question the concept of NP-completeness has been very useful. We define the completeness of TAUTOLOGY-NP using the polynomial time reduction as well. We demonstrate there is a TAUTOLOGY-L language that is not only complete for TAUTOLOGY-NP, but it is also in P.

Cited by 0Open access

The complexity of class TAUTOLOGY-NP

Vega, Frank · Figshare · 2018

P versus NP is considered as one of the most important open problems in computer science. This consists in knowing the answer of the following question: Is P equal to NP? This question was first mentioned in a letter written by John Nash to the National Security Agency in 1955. A precise statement of the P versus NP problem was introduced independently in 1971 by Stephen Cook and Leonid Levin. Since that date, all efforts to find a proof for this problem have failed. TAUTOLOGY-L is a problem of deciding given an instance x of a language L whether every possible appropriate answer for x is actually a solution in L. The class TAUTOLOGY-NP contains those languages TAUTOLOGY-L where L is in NP. Another major complexity class is NP-complete. To attack the P versus NP question the concept of NP-completeness has been very useful. We define the completeness of TAUTOLOGY-NP using the polynomial time reduction as well. We demonstrate there is a TAUTOLOGY-L language that is not only complete for TAUTOLOGY-NP, but it is also in P.

Cited by 0Open access

The complexity of class OTHER-NP

Vega, Frank · Figshare · 2018

P versus NP is considered as one of the most important open problems in computer science. This consists in knowing the answer of the following question: Is P equal to NP? This question was first mentioned in a letter written by John Nash to the National Security Agency in 1955. A precise statement of the P versus NP problem was introduced independently in 1971 by Stephen Cook and Leonid Levin. Since that date, all efforts to find a proof for this problem have failed. OTHER-L is a problem of deciding given a solution y of an instance x in a language L whether x has another solution different of y. The class OTHER-NP contains those languages OTHER-L where L is in NP. Another major complexity class is NP-complete. To attack the P versus NP question the concept of NP-completeness has been very useful. We show a previous known OTHER-NP language which is NP-complete. If any single NP-complete problem can be solved in polynomial time, then every NP problem has a polynomial time algorithm. Therefore, if every OTHER-NP language is in P, then P = NP. Moreover, we show OTHER-SAT and OTHER-3SAT are complete for OTHER-NP. Furthermore, we prove OTHER-SAT is NP-complete as well. Finally, we demonstrate the existence of a trivial OTHER-L language that is not only in OTHER-NP, but it is also in P where L is NP-complete.

Cited by 0Open access

Class Complexity Metric to Predict Understandability

2016

Abstract — This paper presents a new class complexity metric of an Object-Oriented (OO) program which is used to predict the understandability of classes. The propose complexity metric is evaluated theoretically against Weyuker’s properties to analyze the nature of metric and empirically evaluated against three small projects developed by Post Graduate (PG)/Under Graduate (UG) teams. Least Square Regression Analysis technique is performed to arrive at the result and find correlation coefficient of propose metric with the Degree of Understandability. The result indicates that the propose metric is a good predictor of understandability of classes. JHAWK TOOL (Java Code Metrics Tool) were used to evaluate the parameters values involved in propose metric and for analyzing the results of projects, Matlab6.1 and IBM SPSS software were used.

Cited by 0

The complexity of class TAUTOLOGY-NP

Vega, Frank · Figshare · 2018

P versus NP is considered as one of the most important open problems in computer science. This consists in knowing the answer of the following question: Is P equal to NP? This question was first mentioned in a letter written by John Nash to the National Security Agency in 1955. A precise statement of the P versus NP problem was introduced independently in 1971 by Stephen Cook and Leonid Levin. Since that date, all efforts to find a proof for this problem have failed. TAUTOLOGY-L is a problem of deciding given an instance x of a language L whether every possible appropriate answer for x is actually a solution in L. The class TAUTOLOGY-NP contains those languages TAUTOLOGY-L where L is in NP. Another major complexity class is NP-complete. To attack the P versus NP question the concept of NP-completeness has been very useful. We define the completeness of TAUTOLOGY-NP using the polynomial time reduction as well. We demonstrate there is a TAUTOLOGY-L language that is not only complete for TAUTOLOGY-NP, but it is also in P.

Cited by 0Open access

The complexity of class OTHER-NP

Vega, Frank · Figshare · 2018

P versus NP is considered as one of the most important open problems in computer science. This consists in knowing the answer of the following question: Is P equal to NP? This question was first mentioned in a letter written by John Nash to the National Security Agency in 1955. A precise statement of the P versus NP problem was introduced independently in 1971 by Stephen Cook and Leonid Levin. Since that date, all efforts to find a proof for this problem have failed. OTHER-L is a problem of deciding given a solution y of an instance x in a language L whether x has another solution different of y. The class OTHER-NP contains those languages OTHER-L where L is in NP. Another major complexity class is NP-complete. To attack the P versus NP question the concept of NP-completeness has been very useful. We show a previous known OTHER-NP language which is NP-complete. If any single NP-complete problem can be solved in polynomial time, then every NP problem has a polynomial time algorithm. Therefore, if every OTHER-NP language is in P, then P = NP. Moreover, we show OTHER-SAT and OTHER-3SAT are complete for OTHER-NP. Furthermore, we prove OTHER-SAT is NP-complete as well. Finally, we demonstrate the existence of a trivial OTHER-L language that is not only in OTHER-NP, but it is also in P where L is NP-complete.

Cited by 0Open access

Time Complexity and the Class P

The Complexity Of · 2007

> O[t]-time dtm g: 3.1 Analyzing algorithms Let's analyze two algorithms for the language A = f 0 k 1 k jk ? 0 g. Define a single-tape Turing machine M 1 as follows. "On input string x: 1. Scan across the tape and reject if there is a 0 on the right of some 1. 2. Repeat the following as long as there are some 0s and some 1s remaining on the tape: 3. Scan across the tape and check if the total number of 0s and 1s is odd or even. If it is odd, reject. 4. Scan across the tape again, crossing off every other 0 starting from the first 0, and then crossing off every other 1 starting from the first 1. 5. If no 0s and no 1s remain on the tape, accept. Otherwise, reject." To analyze the running time of M 1 , we first observe that stages 1 and 5 are executed at most

Cited by 0