Eliminating unit reductions from LR(k) parsers using minimum contexts

Summary This paper presents a new approach to the design and the proof of bypassed LR(k) parsers; a bypassed LR(k) parser is an LR(k) parser which does not perform any reductions caused by insignificant unit productions. We show that bypassed LR(k) parsers having minimum set of reduction contexts always exist for Knuth LR(k) parsers, but do not necessarily exist for SLR(k) and LALR(k) parsers. As byproducts of our approach, we naturally derive Anderson, Eve and Homing's algorithm [5] and a sufficient condition for the existence of bypassed SLR(1) parsers.     

Methods for the automatic construction of error correcting parsers

Summary Methods for the automatic construction of error handling parsers are presented. The resulting parsers are capable of correcting all syntax errors by insertion and/or deletion of terminal symbols to the right of the error location. Thus, the output of the parser always corresponds to a syntactically valid program. This contributes significantly to the reliability and robustness of a compiler. The speed of parsing correct parts of a program is not affected by the presence of the error handling capability. The correction algorithm is easy to implement. Apart from the parsing tables only one character per parser state is required to control the correction process. The method is applicable to a wide class of stack automata including LL(k), LR(k), SLR(k), and LALR(k) parsers. It is shown that for LL(k) grammars error correction can be obtained as a byproduct of the canonical LL(k) parser generation. A similar result can be obtained for LR(k) grammars if the parser generator is slightly modified. The method has been successfully added to an LALR(1) parser generator.     

Generalized deterministic left to right parsing

Summary A parser model is presented whose structure is a generalization of the well known LR(k) parsers. Various classes of this parser that would be both practical and efficient to use in a compiler are examined. Associated with these classes of parsers is a hierarchy of type-0 grammars, each grammatical class being defined in terms of the form and structure of derivations. In particular, parsers based on a class called deterministic regular parsable (DRP) grammars will detect any errors as soon as possible during a left to right scan of the input. LR(k) grammars are also DRP. Much research related to LR(k) grammars and parsing is also applicable to DRP grammars and their associated parsers.     

Efficient algorithms for regular expression constrained sequence alignment

Imposing constraints is an effective means to incorporate biological knowledge into alignment procedures. As in the PROSITE database, functional sites of proteins can be effectively described as regular expressions. In an alignment of protein sequences it is natural to expect that functional motifs should be aligned together. Due to this motivation, Arslan introduced the regular expression constrained sequence alignment problem and proposed an algorithm which, if implemented naïvely, can take time and space up to O(²|Σ|⁴|V|n²) and O(²|Σ|⁴|V|n), respectively, where Σ is the alphabet, n is the sequence length, and V is the set of states in an automaton equivalent to the input regular expression. In this paper we propose a more efficient algorithm solving this problem which takes O(³|V|n²) time and O(²|V|n) space in the worst case. If |V|=O(logn) we propose another algorithm with time complexity O(²|V|log|V|n²). The time complexity of our algorithms is independent of Σ, which is desirable in protein applications where the formulation of this problem originates; a factor of ²|Σ|=400 in the time complexity of the previously proposed algorithm would significantly affect the efficiency in practice.     

XOR-Based Schemes for Fast Parallel IP Lookups

An IP router must forward packets at gigabit speed in order to guarantee a good quality of service. Two important factors make this task a challenging problem: (i) for each packet, the longest matching prefix in the forwarding table must be quickly computed; (ii) the routing tables contain several thousands of entries and their size grows significantly every year. Because of this, parallel routers have been developed which use several processors to forward packets. In this work we present a novel algorithmic technique which, for the first time, exploits the parallelism of the router also to reduce the size of the routing table. Our method is scalable and requires only minimal additional hardware. Indeed, we prove that any IP routing table T can be split into two subtables T₁ and T₂ such that: (a) |T₁| can be any positive integer k ≤ |T| and |T₂| ≤ |T| - k + 1; (b) the two routing tables can be used separately by two processors so that the IP lookup on T is obtained by simply XOR-ing the IP lookup on the two tables. Our method is independent of the data structure used to implement the lookup search and it allows for a better use of the processors L2 cache. For real routers routing tables, we also show how to achieve simultaneously: (a) |T₁| is roughly 7% of the original table T; (b) the lookup on table T₂ does not require the bestmatching prefix computation.     

Existence and efficient construction of fast Fourier transforms on supersolvable groups

The linear complexityL _K(A) of a matrixA over a fieldK is defined as the minimal number of additions, subtractions and scalar multiplications sufficient to evaluateA at a generic input vector. IfG is a finite group andK a field containing a primitive exp(G)-th root of unity,L _K(G):= min{L _K(A)|A a Fourier transform forKG} is called theK-linear complexity ofG. We show that every supersolvable groupG has amonomial Fourier Transform adapted to a chief series ofG. The proof is constructive and gives rise to an efficient algorithm with running timeO(|G|²log|G|). Moreover, we prove that these Fourier transforms are efficient to evaluate:L _K(G)8.5|G|log|G| for any supersolvable groupG andL _K(G)1.5|G|log|G| for any 2-groupG.     

A scheme for lr(k) parsing with error recovery part iii: error correction

The paper is the third in a series of three papers devoted to a detailed study of LR(k) parsing with error recovery and correction. A new class of syntax errors is introduced, called (k)-local parser defined errors, which suit better than the conventional minimum distance errors for characterization of error detection and recovery in LR(k) parsing. The question whether a given string has n k-local parser defined errors for some integer n is shown to be decidable. Using the formalization of LR(k) parsing and error recovery presented in the first and the second paper in the series it is shown that the canonical LR(k) parser of an LR(k) grammar always has an error recovering extension which is able to produce a correction for any terminal string containing only (k)-local parser defined errors.     

A Fixed-Parameter Approach to 2-Layer Planarization

A bipartite graph is biplanar if the vertices can be placed on two parallel lines (layers) in the plane such that there are no edge crossings when edges are drawn as line segments between the layers. In this paper we study the 2-Layer Planarization problem: Can k edges be deleted from a given graph G so that the remaining graph is biplanar? This problem is NP-complete, and remains so if the permutation of the vertices in one layer is fixed (the 1-Layer Planarization problem). We prove that these problems are fixed-parameter tractable by giving linear-time algorithms for their solution (for fixed k). In particular, we solve the 2-Layer Planarization problem in O(k · 6^k + |G|) time and the 1-Layer Planarization problem in O(3^k · |G|) time. We also show that there are polynomial-time constant-approximation algorithms for both problems.     

A $${\mathcal{O}(|G|n^6)}$$ time extension of inversion transduction grammars

Range concatenation grammars are viewed as a hierarchy of synchronous grammars. It is shown how inversion transduction grammars (ITGs) and extensions thereof, including synchronous tree-adjoining grammars, are captured by the hierarchy, and the expressivity and linguistic relevance of subclasses of the hierarchy are discussed. A O(|G|n⁶){\mathcal{O}(|G|n^6)} time extension of ITGs is proposed. The extension translates cross-serial dependencies into nested ones and handles complex kinds of discontinuous translation units and so-called inside-out alignments. In fact, our O(|G|n⁶){\mathcal{O}(|G|n^6)} time extension generates all possible alignments. It is shown that this additional expressivity comes at the cost of probabilistic parsing.     

A probabilistic algorithm for vertex connectivity of graphs

A probabilistic algorithm is presented which computes the vertex connectivity of an undirected graph G = (V,E) in expected time $\text{O((-log ε|V|}{}^{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{|E|)}$ with error probability at most e provided that |E|<frcase|1/2d|V|² for some universal constant d<1.     

A new recursion-theoretic characterization of the polytime functions

We give a recursion-theoretic characterization of FP which describes polynomial time computation independently of any externally imposed resource bounds. In particular, this syntactic characterization avoids the explicit size bounds on recursion (and the initial function 2^|x|·|y|) of Cobham.     

基于状态回朔技术的规范LR分析算法

LR分析技术以其自身的优点在实际当中有着非常广泛的应用,但是,能够识别LR(1)语言的规范LR分析器由于其下推自动机的复杂性,其实用性受到比较大的限制.通过回朔下推自动机的状态迁移路径能够从根本上解决这一问题.主要讨论了基于状态回朔技术的规范型LR分析器的基本原理与构造技术.     

Eliminating unit productions from LR parsers

Summary In this paper we show how one can improve upon an algorithm by Aho and Ullman [3] for eliminating unit productions from an LR(k) parser so that the elimination concerned can be made in all cases, instead of only in the special case required by [3] where no two unit productions have the same left-hand side. In most practical grammars this special case does not in fact arise. Since the elimination of unit productions both reduces the size of the parser and increases its speed, it is of value to have a general method for achieving this objective.The algorithm provided eliminates from the parser all nonterminals that occur as left-hand sides of unit productions. This substantially contributes to the reduction in size obtained, and also provides a solution to an open problem by Aho and Ullman [3]. An application of the Algorithm to the parser construction method of Pager [19] is considered, and a method is provided for the use of default reductions and the elimination of final states in conjunction with the elimination of unit reductions. The sizes of the parsers obtained using the parser's algorithm are compared with those of Anderson, Eve, and Horning [4].This work was supported by the National Science Foundation under Grant GJ-43362. A shortened version of the paper was presented at the 2nd colloquium on Automata, Languages and Programming, University of Saarbrücken, July 1974     

A Neural Algorithm for the Maximum Clique Problem: Analysis,Experiments, and Circuit Implementation

{In this paper we design and analyze a neural approximation algorithm for the Maximum Clique problem. This algorithm, having as input an arbitrary undirected graph G = \langle V, E\rangle , constructs a finite sequence of Hopfield networks such that the attractor of the last network in the sequence represents a maximal clique of G . We prove that D(G) ⋅ |E ^{\rm c} | , where D(G) = max _{{i,j}\notin E} \min{d _i , d _j } , d _i is the degree of the vertex i of G , and |E ^{\rm c} | denotes the cardinality of the set of edges in the complement graph, is an upper bound to the number of the networks in the sequence. Some experiments made on the second DIMACS benchmark and on random graphs show that: 1. The quality of the solutions found by the algorithm is satisfactory. 2. The theoretical upper bound D(G) ⋅ |E ^{\rm c} | is quite pessimistic. For random graphs we propose an empirical formula that gives a better estimate of the number of networks in the sequence. Moreover, thanks to the simplicity of the algorithm, we are able to design a uniform family of circuits of small size (\approx 10n ² log ₂ n ) that implements it. The circuit, which solves the problems for graphs of at most 32 vertices, has then been programmed on FPGAs (Field Programmable Gate Arrays). An analysis in terms of size and time complexity is given. Received November 10, 1998; revised December 2000.     

Reoptimization of constraint satisfaction problems with approximation resistant predicates

If k = O(log n) and a predicate P is approximation resistant for the reoptimization of the Max-EkCSP-P problem, then, after inserting a truth-value into the predicate and imposing some constraint, there exists a polynomial algorithm with the approximation ratio q(P) = \frac12 - d(P) q(P) = \frac{1}{{2 - d(P)}} , where d(P) = 2 ^{- k}| P ^{- 1}(1) | d(P) = {2^{ - k}}\left| {{P^{ - 1}}(1)} \right| is a “random” threshold approximation ratio of the predicate P. The ratio q(P) is a threshold approximation ratio.     

Periods in Extensions of Words

Let π(w) denote the minimum period of the word w,let w be a primitive word with period π(w) < |w|, and let z be a prefix of w. It is shown that if π(wz) = π(w), then |z| < π(w) − gcd (|w|, |z|). Detailed improvements of this result are also proven. Finally, we show that each primitive word w has a conjugate w′ = vu, where w = uv, such that π(w′) = |w′| and |u| < π(w). As a corollary we give a short proof of the fact that if u,v,w are words such that u ² is a prefix of v ², and v ² is a prefix of w ², and v is primitive, then |w| > 2|u|.     

A syntactic method for analysis of nystagmus and smooth pursuit eye movement

Eye movements are studied in neurophysiology, neurology, ophthalmology, and otology both clinically and in research. In this article, a syntactic method for recognition of horizontal nystagmus and smooth pursuit eye movements is presented. Eye movement signals, which are recorded, for example, electro-oculographically, are transformed into symbol strings of context free grammars. These symbol strings are fed to an LR(k) parser, which detects eye movements as sentences of the formal languages produced by these LR(k) grammars. Since LR(k) grammars have been used, the time required by the whole recognition method is directly proportional to the number of symbols in an input string.     

LEFT TO RIGHT PARSING OF LEXICALIZED TREE-ADJOINING GRAMMARS1

This paper presents an algorithm (a parser) for analyzing sentences according to grammatical constraints expressed in the framework of lexicalized tree-adjoining grammar. For the current grammars of English, the algorithm behaves much better and requires much less time than its worst-case complexity. The main objective of this work is to design a practical parser whose average-case complexity is much superior to its worst case. Most of the previous methods always required the worst-case complexity. The algorithm can be used in two modes. As a recognizer it outputs whether the input sentence is grammatically correct or not. As a parser it outputs a detailed analysis of the grammatically correct sentences. As sentences are read from left to right, information about possible continuations of the sentence is computed. In this sense, the algorithm is called a predictive left to right parser. This feature reduces the average time required to process a given sentence. In the worst case, the parser requires an amount of time proportional to G²n⁶ for a sentence of n words and for a lexicalized tree-adjoining grammar of size G. The worst-case complexity is only reached with pathological (not naturally occurring) grammars and inputs.