scholarly journals Reducing The Space And Time Complexity By The Use of Triangular Matrices

2018 ◽  
Vol 5 (1) ◽  
pp. 1-10
Author(s):  
Zeynep Nihan BERBERLER ◽  
Murat Erşen BERBERLER
Keyword(s):  
Time Complexity ◽  
Triangular Matrices ◽  
Space And Time

scholarly journals Space and time complexity for infinite time Turing machines

2020 ◽  
Vol 30 (6) ◽  
pp. 1239-1255
Author(s):  
Merlin Carl
Keyword(s):  
Time Complexity ◽  
Space Complexity ◽  
Complexity Classes ◽  
Turing Machines ◽  
Infinite Time ◽  
Space And Time ◽  
Open Questions ◽  
Separation Results ◽  
Ordinal Computability

Abstract We consider notions of space by Winter [21, 22]. We answer several open questions about these notions, among them whether low space complexity implies low time complexity (it does not) and whether one of the equalities P=PSPACE, P$_{+}=$PSPACE$_{+}$ and P$_{++}=$PSPACE$_{++}$ holds for ITTMs (all three are false). We also show various separation results between space complexity classes for ITTMs. This considerably expands our earlier observations on the topic in Section 7.2.2 of Carl (2019, Ordinal Computability: An Introduction to Infinitary Machines), which appear here as Lemma $6$ up to Corollary $9$.

FUNCTIONAL PEARL Functional chart parsing of context-free grammars

2004 ◽  
Vol 14 (6) ◽  
pp. 669-680
Author(s):  
PETER LJUNGLÖF
Keyword(s):  
Data Structure ◽  
Time Complexity ◽  
Inference Rules ◽  
Global State ◽  
Bottom Up ◽  
Space And Time ◽  
Chart Parsing ◽  
The Many ◽  
Context Free ◽  
Context Free Grammars

This paper implements a simple and elegant version of bottom-up Kilbury chart parsing (Kilbury, 1985; Wirén, 1992). This is one of the many chart parsing variants, which are all based on the data structure of charts. The chart parsing process uses inference rules to add new edges to the chart, and parsing is complete when no further edges can be added. One novel aspect of this implementation is that it doesn't have to rely on a global state for the implementation of the chart. This makes the code clean, elegant and declarative, while still having the same space and time complexity as the standard imperative implementations.

scholarly journals Worst-case space and time complexity of recursive procedures

1996 ◽  
Vol 11 (2) ◽  
pp. 115-144 ◽  
Author(s):  
Johann Blieberger ◽  
Roland Lieger
Keyword(s):  
Time Complexity ◽  
Worst Case ◽  
Space And Time ◽  
Recursive Procedures

FROM C-CONTINUATIONS TO NEW QUADRATIC ALGORITHMS FOR AUTOMATON SYNTHESIS

2001 ◽  
Vol 11 (06) ◽  
pp. 707-735 ◽  
Author(s):  
J.-M. CHAMPARNAUD ◽  
D. ZIADI
Keyword(s):  
Time Complexity ◽  
Regular Expression ◽  
Time Algorithm ◽  
The Other ◽  
Worst Case ◽  
Partial Derivatives ◽  
Space And Time ◽  
Other Hand ◽  
Deterministic Automata ◽  
The Way

Two classical non-deterministic automata recognize the language denoted by a regular expression: the position automaton which deduces from the position sets defined by Glushkov and McNaughton–Yamada, and the equation automaton which can be computed via Mirkin's prebases or Antimirov's partial derivatives. Let |E| be the size of the expression and ‖E‖ be its alphabetic width, i.e. the number of symbol occurrences. The number of states in the equation automaton is less than or equal to the number of states in the position automaton, which is equal to ‖E‖+1. On the other hand, the worst-case time complexity of Antimirov algorithm is O(‖E‖3· |E|2), while it is only O(‖E‖·|E|) for the most efficient implementations yielding the position automaton (Brüggemann–Klein, Chang and Paige, Champarnaud et al.). We present an O(|E|2) space and time algorithm to compute the equation automaton. It is based on the notion of canonical derivative which makes it possible to efficiently handle sets of word derivatives. By the way, canonical derivatives also lead to a new O(|E|2) space and time algorithm to construct the position automaton.

scholarly journals New Algorithms for Bidirectional Singleton Arc Consistency

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Yonggang Zhang ◽  
Qian Yin ◽  
Xingjun Zhu ◽  
Zhanshan Li ◽  
Sibo Zhang ◽  
...  
Keyword(s):  
Time Complexity ◽  
The Other ◽  
Worst Case ◽  
Space And Time ◽  
Arc Consistency ◽  
Wide Range ◽  
Order Of Magnitude ◽  
Special Circumstances ◽  
New Algorithms

Bidirectional singleton arc consistency (BiSAC) which is an extended singleton arc consistency (SAC) has been proposed recently. The first contribution of this paper is to propose and prove two theorems of BiSAC theoretically (one is a property of BiSAC and the other is the property of allowing the deletion of some BiSAC-inconsistent values). Secondly, based on these properties we present two algorithms, denoted by BiSAC-DF and BiSAC-DP, to enforce BiSAC. Also, we prove their correctness and analyze the space and time complexity of them in detail. Besides, for special circumstances, we show that BiSAC-DF admits a worst-case time complexity inO(en2d4)and a best one inO(en2d3)when the problem is an already BiSAC, while BiSAC-DP also has the same best one when the tightness is small. Finally, experiments on a wide range of CSP instances show BiSAC-DF and BiSAC-DP are usually around one order of magnitude faster than the existing BiSAC-1. For some special instances, BiSAC-DP is about two orders of magnitude efficient.

BRUTE FORCE DETERMINIZATION OF NFAs BY MEANS OF STATE COVERS

2005 ◽  
Vol 16 (03) ◽  
pp. 441-451 ◽  
Author(s):  
J.-M. CHAMPARNAUD ◽  
F. COULON ◽  
T. PARANTHOËN
Keyword(s):  
Time Complexity ◽  
Regular Expression ◽  
Blow Up ◽  
Finite Automata ◽  
A Priori ◽  
Search Algorithms ◽  
Space Complexity ◽  
Brute Force ◽  
Practical Applications ◽  
Space And Time

Finite automata determinization is a critical operation for numerous practical applications such as regular expression search. Algorithms have to deal with the possible blow up of determinization. There exist solutions to control the space and time complexity like the so called "on the fly" determinization. Another solution consists in performing brute force determinization, which is robust and technically fast, although a priori its space complexity constitutes a weakness. However, one can reduce this complexity by perfoming a partial brute force determinization. This paper provides optimizations that consist in detecting classes of unreachable states and transitions of the subset automaton, which leads in average to an exponential reduction of the complexity of brute force and partial brute force determinization.

On the Space and Time Complexity of Functions Computable by Simple Programs

1983 ◽  
Vol 12 (4) ◽  
pp. 708-716 ◽  
Author(s):  
Tat-Hung Chan ◽  
Oscar H. Ibarra
Keyword(s):  
Time Complexity ◽  
Space And Time

SCHEDULING OF THE DAG ASSOCIATED WITH PIPELINE INVERSION OF TRIANGULAR MATRICES

1996 ◽  
Vol 06 (01) ◽  
pp. 13-26 ◽  
Author(s):  
CLEMENTIN TAYOU DJAMEGNI ◽  
MAURICE TCHUENTE
Keyword(s):  
Lower Bound ◽  
Linear Systems ◽  
Time Complexity ◽  
Canonical Basis ◽  
Triangular Matrix ◽  
Dependence Graph ◽  
Triangular Matrices

We are interested in methods which compute the inverse of a triangular matrix A of order n by solving the n linear systems Ax=ei, i=1,…, n, where ei is the i-th element of the canonical basis of Rn. More precisely, we consider the dependence graph associated with algorithms where the entries of matrix A are read only once and used in pipeline for the solution of these systems. We exhibit a new scheduling which induces an algorithm with time complexity T*=2n−1. The number n2/8+O(n) of processors required by this scheduling improves the best previously known bound n2/6+O(n), and is quite close to the lower bound n2/8.5+O(n).

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