Related papers: Inclusion of Unambiguous RE#s is NP-Hard

Regular expressions with backreferences (regex, for short), as supported by most modern libraries for regular expression matching, have an NP-complete matching problem. We define a complexity parameter of regex, called active variable…

We investigate regular realizability (RR) problems, which are the problems of verifying whether intersection of a regular language -- the input of the problem -- and fixed language called filter is non-empty. In this paper we focus on the…

The advantages for the presence of an XML schema for XML documents are numerous. However, many XML documents in practice are not accompanied by a schema or by a valid schema. Relax NG is a popular and powerful schema language, which…

We investigate regular realizability (RR) problems, which are the problems of verifying whether intersection of a regular language -- the input of the problem -- and fixed language called filter is non-empty. We consider two kind of…

A regular realizability (RR) problem is testing nonemptiness of intersection of some fixed language (filter) with given regular language. We study here complexity of RR problems. It appears that for any language L there exists RR problem…

The success of many natural language processing (NLP) tasks is bound by the number and quality of annotated data, but there is often a shortage of such training data. In this paper, we ask the question: "Can we combine a neural network (NN)…

We study regular expressions that use variables, or parameters, which are interpreted as alphabet letters. We consider two classes of languages denoted by such expressions: under the possibility semantics, a word belongs to the language if…

Despite the theoretical significance and wide practical use of regular expressions, the computational complexity of learning them has been largely unexplored. We study the computational hardness of improperly learning regular expressions in…

Several popular language models represent local contexts in an input text $x$ as bags of words. Such representations are naturally encoded by a sequence graph whose vertices are the distinct words occurring in $x$, with edges representing…

We prove the NP-hardness of the problem whether a given word can be derived from a given regular grammar without repeated occurrence of any nonterminal.

We propose regular expression inference (REI) as a challenge for code/language modelling, and the wider machine learning community. REI is a supervised machine learning (ML) and program optimisation task, and poses the problem of finding…

We show NP-completeness for various problems about the existence of arithmetic expression trees. When given a set of operations, inputs, and a target value does there exist an expression tree with those inputs and operations that evaluates…

Organisations are required to show that their procedures and processes satisfy the relevant regulatory requirements. The computational complexity of proving regulatory compliance is known to be generally hard. However, for some of its…

Parsing Expression Grammars are a popular foundation for describing syntax. Unfortunately, several syntax of programming languages are still hard to recognize with pure PEGs. Notorious cases appears: typedef-defined names in C/C++,…

Regular expressions (regexes) are a powerful mechanism for solving string-matching problems. They are supported by all modern programming languages, and have been estimated to appear in more than a third of Python and JavaScript projects.…

An established measure of the expressive power of a given ReLU neural network is the number of linear regions into which it partitions the input space. There exist many different, non-equivalent definitions of what a linear region actually…

We investigate the computational complexity of various problems for simple recurrent neural networks (RNNs) as formal models for recognizing weighted languages. We focus on the single-layer, ReLU-activation, rational-weight RNNs with…

Backreferences and lookaheads are vital features to make classical regular expressions (REGEX) practical. Although these features have been widely used, understanding of the unrestricted combination of them has been limited. Practically,…

We investigate schema languages for unordered XML having no relative order among siblings. First, we propose unordered regular expressions (UREs), essentially regular expressions with unordered concatenation instead of standard…

Results of computational complexity exist for a wide range of phrase structure-based grammar formalisms, while there is an apparent lack of such results for dependency-based formalisms. We here adapt a result on the complexity of…