scholarly journals On the computational complexity of dynamic slicing problems for program schemas

2011 ◽  
Vol 21 (6) ◽  
pp. 1339-1362 ◽  
Author(s):  
SEBASTIAN DANICIC ◽  
ROBERT. M. HIERONS ◽  
MICHAEL R. LAURENCE
Keyword(s):  
Computational Complexity ◽  
Structural Properties ◽  
Program Slicing ◽  
Np Hard ◽  
Complexity Bounds ◽  
Dynamic Slicing ◽  
Original Program ◽  
Control Dependence ◽  
Definition Of ◽  
Restrictive Definition

Given a program, a quotient can be obtained from it by deleting zero or more statements. The field of program slicing is concerned with computing a quotient of a program that preserves part of the behaviour of the original program. All program slicing algorithms take account of the structural properties of a program, such as control dependence and data dependence, rather than the semantics of its functions and predicates, and thus work, in effect, with program schemas. The dynamic slicing criterion of Korel and Laski requires only that program behaviour is preserved in cases where the original program follows a particular path, and that the slice/quotient follows this path. In this paper we formalise Korel and Laski's definition of a dynamic slice as applied to linear schemas, and also formulate a less restrictive definition in which the path through the original program need not be preserved by the slice. The less restrictive definition has the benefit of leading to smaller slices. For both definitions, we compute complexity bounds for the problems of establishing whether a given slice of a linear schema is a dynamic slice and whether a linear schema has a non-trivial dynamic slice, and prove that the latter problem is NP-hard in both cases. We also give an example to prove that minimal dynamic slices (whether or not they preserve the original path) need not be unique.

On the Complexity of Deadlock Recovery

1986 ◽  
Vol 9 (3) ◽  
pp. 323-342
Author(s):  
Joseph Y.-T. Leung ◽  
Burkhard Monien
Keyword(s):  
Computational Complexity ◽  
Polynomial Time ◽  
Arbitrary Number ◽  
The Other ◽  
Np Hard ◽  
Total Cost ◽  
Other Hand ◽  
Input Parameters ◽  
Resource Type

We consider the computational complexity of finding an optimal deadlock recovery. It is known that for an arbitrary number of resource types the problem is NP-hard even when the total cost of deadlocked jobs and the total number of resource units are “small” relative to the number of deadlocked jobs. It is also known that for one resource type the problem is NP-hard when the total cost of deadlocked jobs and the total number of resource units are “large” relative to the number of deadlocked jobs. In this paper we show that for one resource type the problem is solvable in polynomial time when the total cost of deadlocked jobs or the total number of resource units is “small” relative to the number of deadlocked jobs. For fixed m ⩾ 2 resource types, we show that the problem is solvable in polynomial time when the total number of resource units is “small” relative to the number of deadlocked jobs. On the other hand, when the total number of resource units is “large”, the problem becomes NP-hard even when the total cost of deadlocked jobs is “small” relative to the number of deadlocked jobs. The results in the paper, together with previous known ones, give a complete delineation of the complexity of this problem under various assumptions of the input parameters.

scholarly journals Popular Matching in Roommates Setting Is NP-hard

2021 ◽  
Vol 13 (2) ◽  
pp. 1-20
Author(s):  
Sushmita Gupta ◽  
Pranabendu Misra ◽  
Saket Saurabh ◽  
Meirav Zehavi
Keyword(s):  
Computational Complexity ◽  
Np Hard ◽  
Np Complete ◽  
Open Question ◽  
Popular Matching

An input to the P OPULAR M ATCHING problem, in the roommates setting (as opposed to the marriage setting), consists of a graph G (not necessarily bipartite) where each vertex ranks its neighbors in strict order, known as its preference. In the P OPULAR M ATCHING problem the objective is to test whether there exists a matching M * such that there is no matching M where more vertices prefer their matched status in M (in terms of their preferences) over their matched status in M *. In this article, we settle the computational complexity of the P OPULAR M ATCHING problem in the roommates setting by showing that the problem is NP-complete. Thus, we resolve an open question that has been repeatedly and explicitly asked over the last decade.

scholarly journals Carnap’s Structuralist Thesis

2020 ◽  
pp. 383-420
Author(s):  
Georg Schiemer
Keyword(s):  
Present Article ◽  
Structural Properties ◽  
Philosophy Of Mathematics ◽  
Mathematical Structure ◽  
Mathematical Structuralism ◽  
Definition Of ◽  
Philosophical Debates ◽  
Implicit Definitions

This chapter investigates Carnap’s structuralism in his philosophy of mathematics of the 1920s and early 1930s. His approach to mathematics is based on a genuinely structuralist thesis, namely that axiomatic theories describe abstract structures or the structural properties of their objects. The aim in the present article is twofold: first, to show that Carnap, in his contributions to mathematics from the time, proposed three different (but interrelated) ways to characterize the notion of mathematical structure, namely in terms of (i) implicit definitions, (ii) logical constructions, and (iii) definitions by abstraction. The second aim is to re-evaluate Carnap’s early contributions to the philosophy of mathematics in light of contemporary mathematical structuralism. Specifically, the chapter discusses two connections between his structuralist thesis and current philosophical debates on structural abstraction and the on the definition of structural properties.

On the Similarity Search With Hamming Space Sketches

2021 ◽  
pp. 97-127
Author(s):  
Vladimir Mic ◽  
Pavel Zezula
Keyword(s):  
Computational Complexity ◽  
Metric Space ◽  
Similarity Search ◽  
Space Model ◽  
Similarity Query ◽  
Speed Up ◽  
Hamming Space ◽  
Definition Of ◽  
Metric Function ◽  
Selection Of

This chapter focuses on data searching, which is nowadays mostly based on similarity. The similarity search is challenging due to its computational complexity, and also the fact that similarity is subjective and context dependent. The authors assume the metric space model of similarity, defined by the domain of objects and the metric function that measures the dissimilarity of object pairs. The volume of contemporary data is large, and the time efficiency of similarity query executions is essential. This chapter investigates transformations of metric space to Hamming space to decrease the memory and computational complexity of the search. Various challenges of the similarity search with sketches in the Hamming space are addressed, including the definition of sketching transformation and efficient search algorithms that exploit sketches to speed-up searching. The indexing of Hamming space and a heuristic to facilitate the selection of a suitable sketching technique for any given application are also considered.

COMPUTATIONAL AND COMPUTER COMPLEXITY OF ANALOGIC CELLULAR WAVE COMPUTERS

2003 ◽  
Vol 12 (04) ◽  
pp. 539-562 ◽  
Author(s):  
TAMÁS ROSKA
Keyword(s):  
Computational Complexity ◽  
Power Dissipation ◽  
New World ◽  
Computer Architectures ◽  
Universal Machine ◽  
Cellular Array ◽  
Physical Implementation ◽  
Definition Of ◽  
Logic Inference

The CNN Universal Machine is generalized as the latest step in computational architectures: a Universal Machine on Flows. Computational complexity and computer complexity issues are studied in different architectural settings. Three mathematical machines are considered: the universal machine on integers (UMZ), the universal machine on reals (UMR) and the universal machine on flows (UMF). The three machines induce different kinds of computational difficulties: combinatorial, algebraic, and dynamic, respectively. After a broader overview on computational complexity issues, it is shown, following the reasoning related the UMR, that in many cases the size is not the most important parameter related to computational complexity. Emerging new computing and computer architectures as well as their physical implementation suggest a new look on computational and computer complexities. The new analog-and-logic (analogic) cellular array computer paradigm, based on the CNN Universal Machine, and its physical implementation in CMOS and optical technologies, proves experimentally the relevance of the role of accuracy and problem parameter in computational complexity. We introduce also the rigorous definition of computational complexity for UMF and prove an NP class of problems. It is also shown that choosing the spatial temporal elementary instructions, as well as taking into account the area and power dissipation, these choices inherently influence computational complexity and computer complexity, respectively. Comments related to relevance to biology of the UMF are presented in relation to complexity theory. It is shown that algorithms using spatial-temporal continuous elementary instructions (α-recursive functions) represent not only a new world in computing, but also, a more general type of logic inference.

MODEL NET: A REPRESENTATION OF THE STATIC STRUCTURE OF MODELBASE

2007 ◽  
Vol 21 (04) ◽  
pp. 791-807 ◽  
Author(s):  
CHANGSONG QI ◽  
JIGUI SUN
Keyword(s):  
Computational Complexity ◽  
Directed Graph ◽  
Decision Problem ◽  
Formal Definition ◽  
Model Composition ◽  
Static Structure ◽  
Construction Algorithm ◽  
Composite Models ◽  
Definition Of

Model net proposed in this paper is a kind of directed graph used to represent and analyze the static structure of a modelbase. After the formal definition of the model net was given, a construction algorithm is introduced. Then, two simplification algorithms are put forward to show how this approach can reduce the computational complexity of model composition for a specific decision problem. In succession, a model composition algorithm is worked out based on the simplification algorithms. As a result, this algorithm is capable of finding out all the candidate composite models for a specific decision problem. Finally, several advantages of the model net are discussed briefly.

How Many Urban Brownfields are Out There?: An Economic Base Contraction Analysis of 31 U.S. Cities

1998 ◽  
Vol 2 (3) ◽  
pp. 267-273 ◽  
Author(s):  
Robert A. Simons
Keyword(s):  
United States ◽  
Central City ◽  
The United States ◽  
Economic Base ◽  
Central Cities ◽  
Large Cities ◽  
Brownfield Sites ◽  
Definition Of ◽  
Restrictive Definition ◽  
Base Contraction

How many brownfield sites are there in the United States? Although numerous federal and state lists of contaminated lands are known—totaling more than 380,000 sites—there is no comprehensive estimate of unlisted or total brownfield sites. This article uses economic base contraction analysis to provide an estimate of the number and acreage of brownfield sites, by type and as a percentage of the land, in 31 large cities in the United States. This approach recognizes that brownfields are the outcome of years of decline in central-city manufacturing, trade, transportation, and residential uses. Using a moderately restrictive definition of brownfield, there are an estimated 75,000 formerly industrial brownfield sites in these U.S. central cities, on 93,000 acres. This is about 5% of the land area in these communities. Another 20,000 acres are present in these same cities in the form of residential brownfields. These findings imply that the overall number of nonresidential brownfields sites in the United States is at least 500,000 to 600,000 or more.

scholarly journals Computing the Interleaving Distance is NP-Hard

2019 ◽  
Vol 20 (5) ◽  
pp. 1237-1271 ◽  
Author(s):  
Håvard Bakke Bjerkevik ◽  
Magnus Bakke Botnan ◽  
Michael Kerber
Keyword(s):  
Computational Complexity ◽  
Complete Characterization ◽  
Np Hard ◽  
Slight Improvement ◽  
Approximation Factor ◽  
Distance Computation ◽  
Persistence Modules ◽  
Np Complete ◽  
Interleaving Distance

Abstract We show that computing the interleaving distance between two multi-graded persistence modules is NP-hard. More precisely, we show that deciding whether two modules are 1-interleaved is NP-complete, already for bigraded, interval decomposable modules. Our proof is based on previous work showing that a constrained matrix invertibility problem can be reduced to the interleaving distance computation of a special type of persistence modules. We show that this matrix invertibility problem is NP-complete. We also give a slight improvement in the above reduction, showing that also the approximation of the interleaving distance is NP-hard for any approximation factor smaller than 3. Additionally, we obtain corresponding hardness results for the case that the modules are indecomposable, and in the setting of one-sided stability. Furthermore, we show that checking for injections (resp. surjections) between persistence modules is NP-hard. In conjunction with earlier results from computational algebra this gives a complete characterization of the computational complexity of one-sided stability. Lastly, we show that it is in general NP-hard to approximate distances induced by noise systems within a factor of 2.

The Multi-Slice Method of Program Slicing for Fault Location

2014 ◽  
Vol 971-973 ◽  
pp. 1808-1811
Author(s):  
Kun Liang Zhang ◽  
Xiu Ying Peng ◽  
Hao Hua Li
Keyword(s):  
Program Analysis ◽  
Fault Location ◽  
Fault Localization ◽  
Program Slicing ◽  
Localization Method ◽  
Advantages And Disadvantages ◽  
Dynamic Slicing ◽  
Full Analysis ◽  
Software Fault ◽  
Slice Method

Program slicing is a program analysis and understanding of technology. Sequence fault localization refers to the use of specific methods for faults in the program. Currently, the research program fault positioning is more and more people's attention and gets some results which is the more mainstream software fault localization method. Program slicing technique currently used to locate the fault procedures, which primarily to take advantage of dynamic slicing technique. Based on the full analysis of the advantages and disadvantages on the basis of previous work, we propose a flexible slicing rule and give a new method based on the slicing rule.

scholarly journals Computational Complexity of Topological Invariants

2014 ◽  
Vol 58 (1) ◽  
pp. 27-32
Author(s):  
Manuel Amann
Keyword(s):  
Computational Complexity ◽  
Decision Problem ◽  
Topological Invariants ◽  
Np Hard ◽  
Connected Space ◽  
Finite Dimensional ◽  
Lusternik Schnirelmann ◽  
Simply Connected

AbstractWe answer the following question posed by Lechuga: given a simply connected spaceXwith bothH*(X; ℚ) and π*(X) ⊗ ℚ being finite dimensional, what is the computational complexity of an algorithm computing the cup length and the rational Lusternik—Schnirelmann category ofX?Basically, by a reduction from the decision problem of whether a given graph isk-colourable fork≥ 3, we show that even stricter versions of the problems above are NP-hard.

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