A Polynomial Time Extension of Parallel Multiple Context-Free Grammar

2005 ◽  
pp. 177-188 ◽  
Author(s):  
Peter Ljunglöf
Keyword(s):  
Polynomial Time ◽  
Context Free Grammar ◽  
Multiple Context ◽  
Time Extension ◽  
Context Free

scholarly journals Second-position clitics and the syntax-phonology interface: The case of ancient Greek

2016 ◽  
Author(s):  
David M. Goldstein ◽  
Dag T. T. Haug
Keyword(s):  
Ancient Greek ◽  
Context Free Grammar ◽  
Multiple Context ◽  
Yield Functions ◽  
Break Up ◽  
Context Free

In this paper we discuss second position clitics in Ancient Greek, which show a remarkable ability to break up syntactic constituents. We argue against attempts to capture such data in terms of a mismatch between c-structure yield and surface string and instead propose to enrich c-structure by using a multiple context free grammar with explicit yield functions rather than an ordinary CFG.

scholarly journals On the Complexity of the Smallest Grammar Problem over Fixed Alphabets

2020 ◽  
Author(s):  
Katrin Casel ◽  
Henning Fernau ◽  
Serge Gaspers ◽  
Benjamin Gras ◽  
Markus L. Schmid
Keyword(s):  
Polynomial Time ◽  
Approximation Scheme ◽  
Time Algorithm ◽  
Polynomial Time Approximation Scheme ◽  
Context Free Grammar ◽  
Constant Size ◽  
Size Measure ◽  
The Right ◽  
The Impact ◽  
Context Free

AbstractIn the smallest grammar problem, we are given a word w and we want to compute a preferably small context-free grammar G for the singleton language {w} (where the size of a grammar is the sum of the sizes of its rules, and the size of a rule is measured by the length of its right side). It is known that, for unbounded alphabets, the decision variant of this problem is NP-hard and the optimisation variant does not allow a polynomial-time approximation scheme, unless P = NP. We settle the long-standing open problem whether these hardness results also hold for the more realistic case of a constant-size alphabet. More precisely, it is shown that the smallest grammar problem remains NP-complete (and its optimisation version is APX-hard), even if the alphabet is fixed and has size of at least 17. The corresponding reduction is robust in the sense that it also works for an alternative size-measure of grammars that is commonly used in the literature (i. e., a size measure also taking the number of rules into account), and it also allows to conclude that even computing the number of rules required by a smallest grammar is a hard problem. On the other hand, if the number of nonterminals (or, equivalently, the number of rules) is bounded by a constant, then the smallest grammar problem can be solved in polynomial time, which is shown by encoding it as a problem on graphs with interval structure. However, treating the number of rules as a parameter (in terms of parameterised complexity) yields W[1]-hardness. Furthermore, we present an $\mathcal {O}(3^{\mid {w}\mid })$ O ( 3 ∣ w ∣ ) exact exponential-time algorithm, based on dynamic programming. These three main questions are also investigated for 1-level grammars, i. e., grammars for which only the start rule contains nonterminals on the right side; thus, investigating the impact of the “hierarchical depth” of grammars on the complexity of the smallest grammar problem. In this regard, we obtain for 1-level grammars similar, but slightly stronger results.

Framework for rare event detection using Artificial Neural Network based context free grammar

2020 ◽  
Vol 39 (6) ◽  
pp. 8463-8475
Author(s):  
Palanivel Srinivasan ◽  
Manivannan Doraipandian
Keyword(s):  
Neural Network ◽  
Artificial Neural Network ◽  
Event Detection ◽  
Performance Metrics ◽  
Rare Events ◽  
Rare Event ◽  
Video Stream ◽  
Context Free Grammar ◽  
Artificial Neural ◽  
Context Free

Rare event detections are performed using spatial domain and frequency domain-based procedures. Omnipresent surveillance camera footages are increasing exponentially due course the time. Monitoring all the events manually is an insignificant and more time-consuming process. Therefore, an automated rare event detection contrivance is required to make this process manageable. In this work, a Context-Free Grammar (CFG) is developed for detecting rare events from a video stream and Artificial Neural Network (ANN) is used to train CFG. A set of dedicated algorithms are used to perform frame split process, edge detection, background subtraction and convert the processed data into CFG. The developed CFG is converted into nodes and edges to form a graph. The graph is given to the input layer of an ANN to classify normal and rare event classes. Graph derived from CFG using input video stream is used to train ANN Further the performance of developed Artificial Neural Network Based Context-Free Grammar – Rare Event Detection (ACFG-RED) is compared with other existing techniques and performance metrics such as accuracy, precision, sensitivity, recall, average processing time and average processing power are used for performance estimation and analyzed. Better performance metrics values have been observed for the ANN-CFG model compared with other techniques. The developed model will provide a better solution in detecting rare events using video streams.

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