A Pumping Lemma for Permitting Semi-Conditional Languages

Many graph analysis problems can be formulated as formal language-constrained path querying problems where the formal languages are used as constraints for navigational path queries. Recently, the context-free language (CFL) reachability formulation has become very popular and can be used in many areas, for example, querying graph databases, Resource Description Framework (RDF) analysis. However, the generative capacity of context-free grammars (CFGs) is too weak to generate some complex queries, for example, from natural languages, and the various extensions of CFGs have been proposed. Multiple context-free grammar (MCFG) is one of such extensions of CFGs. Despite the fact that, to the best of our knowledge, there is no algorithm for MCFL-reachability, this problem is known to be decidable. This paper is devoted to developing the first such algorithm for the MCFL-reachability problem. The essence of the proposed algorithm is to use a set of Boolean matrices and operations on them to find paths in a graph that satisfy the given constraints. The main operation here is Boolean matrix multiplication. As a result, the algorithm returns a set of matrices containing all information needed to solve the MCFL-reachability problem. The presented algorithm is implemented in Python using GraphBLAS API. An analysis of real RDF data and synthetic graphs for some MCFLs is performed. The study showed that using a sparse format for matrix storage and parallel computing for graphs with tens of thousands of edges the analysis time can be 10–20 minutes. The result of the analysis provides tens of millions of reachable vertex pairs. The proposed algorithm can be applied in problems of static code analysis, bioinformatics, network analysis, as well as in graph databases when a path query cannot be expressed using context-free grammars. The provided algorithm is linear algebra-based, hence, it allows one to use high-performance libraries and utilize modern parallel hardware.

For the purpose of writing and constructing compilers, interpreters and optimizers the parsing of code is mandatory. The syntactic analysis of the input intermediate code into its component parts is known as parsing. And for the implementation of such parsers we need a Context Free Grammar (CFG) which helps to analyses the input code. This paper mainly focuses on extension of the CFG in an EBNF form which describes the parser for intermediate code and different peephole optimization rules. The peephole optimizer basically applies some strategies to perform optimization on the intermediate code based on optimization rules but for that it requires parsers which help to determine the intermediate code and optimization rules accordingly.

The Generalized LR parsing algorithm for context-free grammars is notable for having a decent worst-case running time (cubic in the length of the input string, if implemented efficiently), as well as much better performance on “good” grammars. This paper extends the Generalized LR algorithm to the case of “grammars with left contexts” (M. Barash, A. Okhotin, “An extension of context-free grammars with one-sided context specifications”, Inform. Comput., 2014), which augment the context-free grammars with special operators for referring to the left context of the current substring, along with a conjunction operator (as in conjunctive grammars) for combining syntactical conditions. All usual components of the LR algorithm, such as the parsing table, shift and reduce actions, etc., are extended to handle the context operators. The resulting algorithm is applicable to any grammar with left contexts and has the same worst-case cubic-time performance as in the case of context-free grammars.

In this paper we study the problem of total derivability in context-free, noncontracting, and context-sensitive grammars. Given a grammar and a terminal word, one has to determine whether there exists a derivation of this word which uses each production no less than a given number of times. It is proved that the problem of total derivability of the emptyword in a context-free grammar is NP-complete. For noncontracting and context-sensitive grammars it is polynomially decidable for words of length 1, and it is NP-complete for every fixed word of length at least 2. Analagous results are obtained for another variant of the problem of total derivability when restrictions are placed on the amount of uses of nonterminals in the derivation.

Like most of the South-Asian languages Urdu and Sindhi are partial word order languages. Conventional syntax representation models like Context Free Grammars are not capable enough to cope with partial word order syntax. Linear Specification Language (LSL) is an extension of Context-Free Grammars (CFGs) which allows arbitrary partial order (free word order) on the right hand side of grammar rule. Partial word order in LSL is handled by using different types of linear precedence (LP) constraints. LSL by using LP constraints is capable enough to represent the syntax of partial word order sentence. Issues related to represent Urdu/Sindhi language sentences with their constituent parts in LSL are discussed. LSL versions for different types of Urdu and Sindhi sentences are presented.

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?

On the degrees of non-regularity and non-context-freeness

We introduce annotated grammars, an extension of context-free grammars which allows annotations on terminals. Our model extends the standard notion of regular spanners, and is more expressive than the extraction grammars recently introduced by Peterfreund. We study the enumeration problem for annotated grammars: fixing a grammar, and given a string as input, enumerate all annotations of the string that form a word derivable from the grammar. Our first result is an algorithm for unambiguous annotated grammars, which preprocesses the input string in cubic time and enumerates all annotations with output-linear delay. This improves over Peterfreund's result, which needs quintic time preprocessing to achieve this delay bound. We then study how we can reduce the preprocessing time while keeping the same delay bound, by making additional assumptions on the grammar. Specifically, we present a class of grammars which only have one derivation shape for all outputs, for which we can enumerate with quadratic time preprocessing. We also give classes that generalize regular spanners for which linear time preprocessing suffices.

Automata, Logic and Semantics In 1973, V. Virkkunen proved that propagating scattered context grammars which use leftmost derivations are as powerful as context-sensitive grammars. This paper brings a significantly simplified proof of this result.

Alternation is a generalized principle of nondeterminism. The alternating turing machine is used to characterize the polynomial hierarchy. In this paper we show, that a hierarchy can be characterized with alternating pushdown automata, which we expect to be strict in contrast to a hierarchy with alternating finite automata or alternating space bounded automata. We describe a similar oracle hierarchy over the context-free languages, for which we construct complete languages. We show, that each level of the hierarchy with alternating pushdown automata is included in the corresponding level of the oracle hierarchy and that the logarithmic closure over both levels is the corresponding level of the polynomial hierarchy with one alternation less.The principle of the alternation is also transfered to grammars. Hereby we prove, that the hierarchy with alternating context-free grammars is identical with the oracle hierarchy over the context-free languages and that in case of unbounded alternation context-free and context-sensitive grammars have the same power.KeywordsFinite AutomatonUniversal StateSentential FormPolynomial HierarchyExistential VariableThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Most of this book (the first 148 pages) is an English version of an introduction to linguistics originally published in Russian in 1969. This material has been expanded into a more standard-sized book for the English-speaking market by tacking on three articles on special topics in linguistics published elsewhere by one or both co-authors; but each of these articles is already available in English translation, and the book stands or falls by the usefulness of its first part. When Gladkij and Mel'~uk wrote their book in the late 1960s, linguistics was little known, even in the USA where most of it had been created not long before. I guess that it was a fairly remarkable achievement on their part to discover and master this exotic discipline (and, in Gladkij 's case, to make a number of original contributions to it), and then to make it known to their fellow-countrymen. However, whether it makes good sense to bring out an English version of the book in the 1980s is a different matter. I must say that I feel the answer is no, for many reasons. In the first place, linguistics has moved on since the 1960s. Gladkij and Mel'~uk's book deals ahnost exclusively with the hierarchy of types of language, defined in terms of types of grammar (unrestricted rewrite systems, context-sensitive grammars, context-free grammars, one-sided linear grammars), with a small amount on the relationship with types of automata, on decidability theorems, and a few other matters. topic of parsing and formalisms with special relevance for automatic language processing, such as the ATN are not mentioned. In 1969, one would not have expected them to be; in the 1980s, these are surely indispensable components even in an introduction to mathematical (as opposed to computat ional) linguistics. Gladkij and Mel'~uk are quite explicit about the fact that they have made no attempt to bring the book up to date: The manuscript of the Russian version of this book was completed in 1967 and we are not in a position to revise it now . . . . Even a mere list of references would be out of the question. Secondly, the book relies heavily on Russian-language examples which are lost on an English reader. Thus, early chapters largely revolve round a largish formal grammar produced by the authors in order to generate the complex range of Russian participles. It must have been a significant virtue of the original book that it demonstrated how the concepts of linguistics could be made to achieve a novel task relating specifically to the readers ' own language, but for a British or American student the result is that ideas many people find difficult at the best of times are rendered wholly opaque. And, finally, Gladkij and Mel'~uk just are not very good at writing for an unknowledgeable audience. They make their formal rules notationally much more complex and exotic-looking than they need be to a fellow mathematician, a trivial matter, but for an unconfident student very unfortunate. On page 25 they use the term monoid without, I think, ever explaining what it means (there is no index, so it is hard to check); on page 81 they use a technical term of their own which is first defined on page 122. fact is that there are now enough English-language books that do the same job as this book and do it much better.

Motivated by the blackboard model of artificial intelligence we introduce the concept of context-free cooperating/distributed grammar systems with hypothesis languages. We prove that these grammar systems have the same generative power as context-sensitive grammars.

We present a formal model for stratificational linguistics, and examine its properties such as generative power, complexity of recognition and descriptional complexity. By relating stratificational grammars to control grammars and Szilard languages, we obtain a table of language families generated by stratificational grammars under several restrictions of linguistic interest. In the process, we show that context-sensitive control grammars with leftmost derivations are no more powerful than context-free ones, and, using this, resolve two open problems of Ginsburg and Spanier. Throughout the paper, formal results are interpreted in terms of their significance for linguistic theory and practice.

In this paper, we mainly study the relation between scattered context grammars, which are an example for regulated context-free rewriting devices, and context-sensitive grammars. Emphasis is laid upon both normal form characterizations of context-sensitive grammars and an argument in how far scattered context grammars are stronger, with respect to generative capacity than unordered scattered context grammars.

Some restrictive devices for context-free grammars