A Graphical Model for Context-Free Grammar Parsing

Linear Algebra in Dioids: A Survey of Recent Results

This chapter is concerned with the Boolean matrix approach to problems concerning the existence and determination of paths in directed graphs.

Mining web log datasets has been extensively studied using Frequent Pattern Mining (FPM) and its various other forms. Identifyingfrequent patterns in different sequences can help in analyzing the most common sub-sequences (e.g., the pages visitedtogether). However, this approach would not be able to identify general structures spanning over multiple sequences. In responseto understanding general structures, we introduce a new form of sequential pattern mining called super-sequence frequent patternmining (SS-FPM). In contrast to sub-sequences determined by FPM, SS-FPM determines the super-sequences that can containthe common parts from different sequences. This can be useful in understanding the general behavior/flow of users in web usagemining, classifying web pages and users, making predictions etc. In essence, finding frequent super-sequence patterns turnsout to be related to the well-known heaviest (longest) path problem in graphs, which is known to be NP-hard. Accordingly,we transform a given sequential dataset into a sequence graph and formulate the problem as k-hop heaviest path problem. Wethen propose an efficient heuristic called sequence matrix method using dynamic programming techniques. We compared ourmethod to the existing Heavypath method. The results show that our method is more efficient especially on large datasets.

In the minimum constraint removal problem, we are given a set of overlapping geometric objects as obstacles in the plane, and we want to find the minimum number of obstacles that must be removed to reach a target point t from the source point s by an obstacle-free path. The problem is known to be intractable and no sub-linear approximations are known even for simple obstacles such as rectangles and disks. The main result of our paper is an approximation framework that gives an O(nα(n))-approximation for polygonal obstacles, where α(n) denotes the inverse Ackermann's function. For pseudodisks and rectilinear polygons, the same technique achieves an O(n)-approximation. The technique also gives O(n)-approximation for the minimum color path problem in graphs. We also present some inapproximability results for the geometric constraint removal problem.

Compiler Design is one of the core courses of Computer Science and Engineering. Syntax Analyzer or Parser is important phase in designing the compiler. So while designing this phase of the compiler, students must have thorough knowledge about the types of parser such as LL(1), SLR, Canonical LR and LALR. In the parser phase, the parsing table is built for given Context Free Grammar (CFG). While implementing this parsing phase in laboratory session, two Free Open Source Software (FOSS) - JFLAP and Parsing Emulator, are considered to explain the types of parser and building the parsing table for the CFG using these parser types. JFLAP is software for experimenting with formal languages topics including nondeterministic finite automata, nondeterministic pushdown automata, multi-tape Turing machines, several types of grammars, parsing, and Lsystems. So this tool is considered for parsing phase of Compiler. JFLAP tool is used to explain the steps to be followed to solve the given problem using the parsing technique. Parsing simulator is a software which implements the parsing table for the Context Free Grammars in tool. This simulator is used to generate parsing table (LL1, SLR, LR, and LALR). Parsing Emulator tool is used for practicing the problem statement given in the tool. In current study, use of FOSS such as JFLAP and Parsing Emulator is considered for teaching parser types to improve problem solving ability. The Learning Objectives (LOs) of this study are: To build the parsing table for given CFG using LL(1) and SLR parser (LO1) and to parse the given string using LL(1) and SLR parser (LO2). The research questions for this study are – whether the use of FOSS improves the problem solving ability of the students? and whether gender bias is there in education? Two groups post-test method is considered to check the effectiveness of this use of FOSS in learning the parser types. Also the students’ perception about this method is also considered. The result shows that the students’ problem solving ability of experimental group is improved as compared to the control group irrespective of gender. Keywords- FOSS (Free Open Source Software) JFLAP, Parsing Emulator, Bloom’s Taxonomy, Post-test, t-Test.

We consider non-self-embedding (NSE) context-free grammars as a representation of regular sets.We point out its advantages with respect to more classical representations by finite automata, in particular when considering the efficient realization of the rational operations. We give a characterization in terms of composition of regular grammars and state relationships between NSE grammars and push-down automata. Finally we show a polynomial algorithm to decide whether a context-free grammars is self-embedding or not.

Reversible pushdown automata are deterministic pushdown automata having the property that any configuration occurring in any computation has exactly one predecessor. In this paper, the computational capacity of reversible computations in pushdown automata is investigated and turns out to lie properly in between the regular and deterministic context-free languages. Furthermore, it can be shown that a deterministic context-free language cannot be accepted reversibly if more than realtime is necessary for acceptance. Closure properties as well as decidability questions for reversible pushdown automata are studied. Finally, the question of whether a given (nondeterministic) pushdown automaton can be algorithmically tested for reversibility is answered in the affirmative, whereas it is shown to be undecidable whether the language accepted by a given nondeterministic pushdown automaton is reversible.

We consider the producer/consumer Petri net and the context-free formal language that it generates. Nonregularity of the language is proved, the corresponding pushdown automaton and context-free grammar are obtained. The connection with the Dyck formal language is pointed out.

We present a collection of new and enhanced tools for experimenting with concepts in formal languages and automata theory. New tools, written in Java, include JFLAP for creating and simulating finite automata, pushdown automata and Turing machines; Pâté for parsing restricted and unrestricted grammars and transforming context-free grammars to Chomsky Normal Form; and PumpLemma for proving specific languages are not regular. Enhancements to previous tools LLparse and LRparse, instructional tools for parsing LL(1) and LR(1) grammars, include parsing LL(2) grammars, displaying parse trees, and parsing any context-free grammar with conflict resolution.

In this article we study the time complexity of the recognition problem for some “moderate” extensions of context-free grammars or pushdown automata. It is well known that, for a given context-free grammar G, the recognition problem “x ∈ L(G)” can be decided in 0(|x|)3 steps by a suitable algorithm. How do extensions behave in this respect? In particular, do they admit recognition algorithms whose time is polynomially bounded by the length of the input?

From the Publisher: This text makes in-depth explorations of a broad range of theoretical topics in computer science. It plunges into the applications of the abstract concepts in order to confront and address the skepticism of readers, and instill in them an appreciation for the usefulness of theory. A two-part presentation integrates logic and formal language—both with applications. Chapter topics cover mathematical preliminaries, propositional logic, proving things: why and how, predicate logic, proving with predicates, program verification, logic programming, language models for computer science, language models, finite automata and their languages, regular expressions, Lex: a tool for building lexical scanners, context-free grammars, pushdown automata and parsing, and turing machines. For future computer scientists.

2 - State of the art: grammatical inference

We consider the fine-grained complexity of sparse graph problems that currently have O(mn) time algorithms, where m is the number of edges and n is the number of vertices in the input graph. This class includes several important path problems on both directed and undirected graphs, including APSP, MWC (Minimum Weight Cycle), Radius, Eccentricities, BC (Betweenness Centrality), etc. We introduce the notion of a sparse reduction which preserves the sparsity of graphs, and we present near linear-time sparse reductions between various pairs of graph problems in the O(mn) class. There are many sub-cubic reductions between graph problems in the O(mn) class, but surprisingly few of these preserve sparsity. In the directed case, our results give a partial order on a large collection of problems in the O(mn) class (along with some equivalences), and many of our reductions are very nontrivial. In the undirected case we give two nontrivial sparse reductions: from MWC to APSP, and from unweighted ANSC (all nodes shortest cycles) to unweighted APSP. We develop a new ‘bit-sampling’ method for these sparse reductions on undirected graphs, which also gives rise to improved or simpler algorithms for cycle finding problems in undirected graphs. We formulate the the notion of MWC hardness, which is based on the assumption that a minimum weight cycle in a directed graph cannot be computed in time polynomially smaller than mn. Our sparse reductions for directed path problems in the O(mn) class establish that several problems in this class, including 2-SiSP (second simple shortest path), s-t Replacement Paths, Radius, Eccentricities and BC are MWC hard. Our sparse reductions give MWC hardness a status for the O(mn) class similar to 3SUM hardness for the quadratic class, since they show sub-mn hardness for a large collection of fundamental and well-studied graph problems that have maintained an O(mn) time bound for over half a century. We also identify Eccentricities and BC as key problems in the O(mn) class which are simultaneously MWC-hard, SETH-hard and k-DSH-hard, where SETH is the Strong Exponential Time Hypothesis, and k-DSH is the hypothesis that a dominating set of size k cannot be computed in time polynomially smaller than nk. Our framework using sparse reductions is very relevant to real-world graphs, which tend to be sparse and for which the O(mn) time algorithms are the ones typically used in practice, and not the O(n3) time algorithms.

We prove: 1) every language accepted by two-way nondeterministic pushdown automaton can be recognized on RAM in O(n3/log n) time; 2) every language accepted by two-way loop-free pushdown automaton can be recognized in O(n3/log2n) time; 3) every context-free language can be recognized on-line in O(n3/log2n) time. We improve the results of [1,7,4].

k-shortest path problem (KSP) is a more general form of the classical shortest path problem in graph. Its task is no longer to find the shortest path between two vertices, but to find the shortest k paths. So far, the reported KSP-algorithms only considers finding shortest k paths with regard to a single criterion, while far more application scenarios of the KSP require to determine k paths by taking more criteria into account. This article formulates the KSP as a multi-objective optimization problem. In consideration of the problem's property and genetic algorithm's great success in multi-objective optimization, the genetic algorithm is utilized as the optimization tool. The genotype is directly represented as the form of natural routing. In order to make the related genetic operators risk-free, the conception of gene-bank is introduced. And the crossover and mutation are both implemented based on the introduced gene-bank. The proposed genetic algorithm is tested on an undirected graph of 9-vertex/65-edge. The testing result shows that, our proposed algorithm is valid and outperforms some other swarm intelligence-based algorithms in terms of the obtained paths' quality.