Formal Properties of XML Grammars and Languages

XML documents are described by a document type definition (DTD). An XML-grammar is a formal grammar that captures the syntactic features of a DTD. We investigate properties of this family of grammars. We show that every XML-language basically has a unique XML-grammar. We give two characterizations of languages generated by XML-grammars, one is set-theoretic, the other is by a kind of saturation property. We investigate decidability problems and prove that some properties that are undecidable for general context-free languages become decidable for XML-languages. We also characterize those XML-grammars that generate regular XML-languages.Comment: 24 page

Matrix Graph Grammars

This book objective is to develop an algebraization of graph grammars. Equivalently, we study graph dynamics. From the point of view of a computer scientist, graph grammars are a natural generalization of Chomsky grammars for which a purely algebraic approach does not exist up to now. A Chomsky (or string) grammar is, roughly speaking, a precise description of a formal language (which in essence is a set of strings). On a more discrete mathematical style, it can be said that graph grammars -- Matrix Graph Grammars in particular -- study dynamics of graphs. Ideally, this algebraization would enforce our understanding of grammars in general, providing new analysis techniques and generalizations of concepts, problems and results known so far.Comment: 321 pages, 75 figures. This book has is publisehd by VDM verlag, ISBN 978-363921255

Linear Parsing Expression Grammars

PEGs were formalized by Ford in 2004, and have several pragmatic operators (such as ordered choice and unlimited lookahead) for better expressing modern programming language syntax. Since these operators are not explicitly defined in the classic formal language theory, it is significant and still challenging to argue PEGs' expressiveness in the context of formal language theory.Since PEGs are relatively new, there are several unsolved problems.One of the problems is revealing a subclass of PEGs that is equivalent to DFAs. This allows application of some techniques from the theory of regular grammar to PEGs. In this paper, we define Linear PEGs (LPEGs), a subclass of PEGs that is equivalent to DFAs. Surprisingly, LPEGs are formalized by only excluding some patterns of recursive nonterminal in PEGs, and include the full set of ordered choice, unlimited lookahead, and greedy repetition, which are characteristic of PEGs. Although the conversion judgement of parsing expressions into DFAs is undecidable in general, the formalism of LPEGs allows for a syntactical judgement of parsing expressions.Comment: Parsing expression grammars, Boolean finite automata, Packrat parsin

On Measuring Non-Recursive Trade-Offs

We investigate the phenomenon of non-recursive trade-offs between descriptional systems in an abstract fashion. We aim at categorizing non-recursive trade-offs by bounds on their growth rate, and show how to deduce such bounds in general. We also identify criteria which, in the spirit of abstract language theory, allow us to deduce non-recursive tradeoffs from effective closure properties of language families on the one hand, and differences in the decidability status of basic decision problems on the other. We develop a qualitative classification of non-recursive trade-offs in order to obtain a better understanding of this very fundamental behaviour of descriptional systems

A Bibliography on Fuzzy Automata, Grammars and Lanuages

This bibliography contains references to papers on fuzzy formal languages, the generation of fuzzy languages by means of fuzzy grammars, the recognition of fuzzy languages by fuzzy automata and machines, as well as some applications of fuzzy set theory to syntactic pattern recognition, linguistics and natural language processing

The Grail theorem prover: Type theory for syntax and semantics

As the name suggests, type-logical grammars are a grammar formalism based on logic and type theory. From the prespective of grammar design, type-logical grammars develop the syntactic and semantic aspects of linguistic phenomena hand-in-hand, letting the desired semantics of an expression inform the syntactic type and vice versa. Prototypical examples of the successful application of type-logical grammars to the syntax-semantics interface include coordination, quantifier scope and extraction.This chapter describes the Grail theorem prover, a series of tools for designing and testing grammars in various modern type-logical grammars which functions as a tool . All tools described in this chapter are freely available

Verification of PCP-Related Computational Reductions in Coq

We formally verify several computational reductions concerning the Post correspondence problem (PCP) using the proof assistant Coq. Our verifications include a reduction of a string rewriting problem generalising the halting problem for Turing machines to PCP, and reductions of PCP to the intersection problem and the palindrome problem for context-free grammars. Interestingly, rigorous correctness proofs for some of the reductions are missing in the literature

Comparing and evaluating extended Lambek calculi

Lambeks Syntactic Calculus, commonly referred to as the Lambek calculus, was innovative in many ways, notably as a precursor of linear logic. But it also showed that we could treat our grammatical framework as a logic (as opposed to a logical theory). However, though it was successful in giving at least a basic treatment of many linguistic phenomena, it was also clear that a slightly more expressive logical calculus was needed for many other cases. Therefore, many extensions and variants of the Lambek calculus have been proposed, since the eighties and up until the present day. As a result, there is now a large class of calculi, each with its own empirical successes and theoretical results, but also each with its own logical primitives. This raises the question: how do we compare and evaluate these different logical formalisms? To answer this question, I present two unifying frameworks for these extended Lambek calculi. Both are proof net calculi with graph contraction criteria. The first calculus is a very general system: you specify the structure of your sequents and it gives you the connectives and contractions which correspond to it. The calculus can be extended with structural rules, which translate directly into graph rewrite rules. The second calculus is first-order (multiplicative intuitionistic) linear logic, which turns out to have several other, independently proposed extensions of the Lambek calculus as fragments. I will illustrate the use of each calculus in building bridges between analyses proposed in different frameworks, in highlighting differences and in helping to identify problems.Comment: Empirical advances in categorial grammars, Aug 2015, Barcelona, Spain. 201

On the relationship between the LL(k) and LR(k) grammars

In the literature various proofs of the inclusion of the class of LL(k) grammars into the class of LR(k) grammars can be found. Some of these proofs are not correct, others are informal, semi-formal or contain flaws. Some of them are correct but the proof is less straightforward than demonstrated here