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

Speech Recognition by Composition of Weighted Finite Automata

We present a general framework based on weighted finite automata and weighted finite-state transducers for describing and implementing speech recognizers. The framework allows us to represent uniformly the information sources and data structures used in recognition, including context-dependent units, pronunciation dictionaries, language models and lattices. Furthermore, general but efficient algorithms can used for combining information sources in actual recognizers and for optimizing their application. In particular, a single composition algorithm is used both to combine in advance information sources such as language models and dictionaries, and to combine acoustic observations and information sources dynamically during recognition.Comment: 24 pages, uses psfig.st

Descriptional complexity of cellular automata and decidability questions

We study the descriptional complexity of cellular automata (CA), a parallel model of computation. We show that between one of the simplest cellular models, the realtime-OCA. and "classical" models like deterministic finite automata (DFA) or pushdown automata (PDA), there will be savings concerning the size of description not bounded by any recursive function, a so-called nonrecursive trade-off. Furthermore, nonrecursive trade-offs are shown between some restricted classes of cellular automata. The set of valid computations of a Turing machine can be recognized by a realtime-OCA. This implies that many decidability questions are not even semi decidable for cellular automata. There is no pumping lemma and no minimization algorithm for cellular automata

On the Expressiveness of Languages for Complex Event Recognition

Complex Event Recognition (CER for short) has recently gained attention as a mechanism for detecting patterns in streams of continuously arriving event data. Numerous CER systems and languages have been proposed in the literature, commonly based on combining operations from regular expressions (sequencing, iteration, and disjunction) and relational algebra (e.g., joins and filters). While these languages are naturally first-order, meaning that variables can only bind single elements, they also provide capabilities for filtering sets of events that occur inside iterative patterns; for example requiring sequences of numbers to be increasing. Unfortunately, these type of filters usually present ad-hoc syntax and under-defined semantics, precisely because variables cannot bind sets of events. As a result, CER languages that provide filtering of sequences commonly lack rigorous semantics and their expressive power is not understood. In this paper we embark on two tasks: First, to define a denotational semantics for CER that naturally allows to bind and filter sets of events; and second, to compare the expressive power of this semantics with that of CER languages that only allow for binding single events. Concretely, we introduce Set-Oriented Complex Event Logic (SO-CEL for short), a variation of the CER language introduced in [Grez et al., 2019] in which all variables bind to sets of matched events. We then compare SO-CEL with CEL, the CER language of [Grez et al., 2019] where variables bind single events. We show that they are equivalent in expressive power when restricted to unary predicates but, surprisingly, incomparable in general. Nevertheless, we show that if we restrict to sets of binary predicates, then SO-CEL is strictly more expressive than CEL. To get a better understanding of the expressive power, computational capabilities, and limitations of SO-CEL, we also investigate the relationship between SO-CEL and Complex Event Automata (CEA), a natural computational model for CER languages. We define a property on CEA called the *-property and show that, under unary predicates, SO-CEL captures precisely the subclass of CEA that satisfy this property. Finally, we identify the operations that SO-CEL is lacking to characterize CEA and introduce a natural extension of the language that captures the complete class of CEA under unary predicates

A Grammatical Inference Approach to Language-Based Anomaly Detection in XML

False-positives are a problem in anomaly-based intrusion detection systems. To counter this issue, we discuss anomaly detection for the eXtensible Markup Language (XML) in a language-theoretic view. We argue that many XML-based attacks target the syntactic level, i.e. the tree structure or element content, and syntax validation of XML documents reduces the attack surface. XML offers so-called schemas for validation, but in real world, schemas are often unavailable, ignored or too general. In this work-in-progress paper we describe a grammatical inference approach to learn an automaton from example XML documents for detecting documents with anomalous syntax. We discuss properties and expressiveness of XML to understand limits of learnability. Our contributions are an XML Schema compatible lexical datatype system to abstract content in XML and an algorithm to learn visibly pushdown automata (VPA) directly from a set of examples. The proposed algorithm does not require the tree representation of XML, so it can process large documents or streams. The resulting deterministic VPA then allows stream validation of documents to recognize deviations in the underlying tree structure or datatypes.Comment: Paper accepted at First Int. Workshop on Emerging Cyberthreats and Countermeasures ECTCM 201

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