Intercalation properties of context-free languages

Context-freedom of a language implies certain intercalation properties known as pumping or iteration lemmas. Although the question of a converse result for some of the properties has been studied, it is still not entirely clear how these properties are related, which are the stronger ones and which are weaker;Among the intercalation properties for context-free languages the better known are the general pumping conditions (generalized Ogden\u27s, Ogden\u27s and classic pumping conditions), Sokolowski-type conditions (Sokolowski\u27s and Extended Sokolowski\u27s conditions) and the Interchange condition. We present a rather systematic investigation of the relationships among these properties; it turns out that the three types of properties, namely pumping, Sokolowski-type and interchange, above are independent. However, the interchange condition is strictly stronger than the Sokolowski\u27s condition;Intercalation properties of some subclasses of context-free languages are also studied. We prove a pumping lemma and an Ogden\u27s lemma for nonterminal bounded languages and show that none of these two conditions is sufficient. We also investigate three of Igarashi\u27s pumping conditions for real-time deterministic context-free languages and show that these conditions are not sufficient either. Furthermore, we formulate linear analogues of the general pumping and interchange conditions and then compare them to the general context-free case. The results show that these conditions are also independent

Collective Phenomena and Non-Finite State Computation in a Human Social System

We investigate the computational structure of a paradigmatic example of distributed social interaction: that of the open-source Wikipedia community. We examine the statistical properties of its cooperative behavior, and perform model selection to determine whether this aspect of the system can be described by a finite-state process, or whether reference to an effectively unbounded resource allows for a more parsimonious description. We find strong evidence, in a majority of the most-edited pages, in favor of a collective-state model, where the probability of a "revert" action declines as the square root of the number of non-revert actions seen since the last revert. We provide evidence that the emergence of this social counter is driven by collective interaction effects, rather than properties of individual users.Comment: 23 pages, 4 figures, 3 tables; to appear in PLoS ON

Comparator automata in quantitative verification

The notion of comparison between system runs is fundamental in formal verification. This concept is implicitly present in the verification of qualitative systems, and is more pronounced in the verification of quantitative systems. In this work, we identify a novel mode of comparison in quantitative systems: the online comparison of the aggregate values of two sequences of quantitative weights. This notion is embodied by {\em comparator automata} ({\em comparators}, in short), a new class of automata that read two infinite sequences of weights synchronously and relate their aggregate values. We show that {aggregate functions} that can be represented with B\"uchi automaton result in comparators that are finite-state and accept by the B\"uchi condition as well. Such {\em $\omega$-regular comparators} further lead to generic algorithms for a number of well-studied problems, including the quantitative inclusion and winning strategies in quantitative graph games with incomplete information, as well as related non-decision problems, such as obtaining a finite representation of all counterexamples in the quantitative inclusion problem. We study comparators for two aggregate functions: discounted-sum and limit-average. We prove that the discounted-sum comparator is $\omega$-regular iff the discount-factor is an integer. Not every aggregate function, however, has an $\omega$-regular comparator. Specifically, we show that the language of sequence-pairs for which limit-average aggregates exist is neither $\omega$-regular nor $\omega$-context-free. Given this result, we introduce the notion of {\em prefix-average} as a relaxation of limit-average aggregation, and show that it admits $\omega$-context-free comparators

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

Generalizing input-driven languages: theoretical and practical benefits

Regular languages (RL) are the simplest family in Chomsky's hierarchy. Thanks to their simplicity they enjoy various nice algebraic and logic properties that have been successfully exploited in many application fields. Practically all of their related problems are decidable, so that they support automatic verification algorithms. Also, they can be recognized in real-time. Context-free languages (CFL) are another major family well-suited to formalize programming, natural, and many other classes of languages; their increased generative power w.r.t. RL, however, causes the loss of several closure properties and of the decidability of important problems; furthermore they need complex parsing algorithms. Thus, various subclasses thereof have been defined with different goals, spanning from efficient, deterministic parsing to closure properties, logic characterization and automatic verification techniques. Among CFL subclasses, so-called structured ones, i.e., those where the typical tree-structure is visible in the sentences, exhibit many of the algebraic and logic properties of RL, whereas deterministic CFL have been thoroughly exploited in compiler construction and other application fields. After surveying and comparing the main properties of those various language families, we go back to operator precedence languages (OPL), an old family through which R. Floyd pioneered deterministic parsing, and we show that they offer unexpected properties in two fields so far investigated in totally independent ways: they enable parsing parallelization in a more effective way than traditional sequential parsers, and exhibit the same algebraic and logic properties so far obtained only for less expressive language families

Locating ethnicity and health: exploring concepts and contexts

With the rapid development of ethnicity and health as a field of sociological research, this paper seeks to re-evaluate the development of ideas around ethnicity, 'race' and culture and consider how they have been applied to the question of health. Ethnicity as a social characteristic is contingent on the situation in which it is manifest. The process of marking 'other' ethnic groups includes stereotyping and racialisation, a process through which 'racial' or ethnic differences predominate to the exclusion of a consideration of social, economic and power relations. In the British context, the history of empire and medicine's justification of racist treatment of enslaved and colonised people, is relevant to understanding how ethnic and cultural differences have come to be essentialised and pathologised. Immigration to Britain only became a mass phenomenon after World War II, with settlement patterns following employment opportunities and kinship alliances. The state has a longstanding history of 'managing' diversity, sometimes essentialising differences between groups, at other times tackling disadvantage and discrimination experiences through policy action. Sociologists of health were slow to study ethnicity, with initial research coming from tropical disease specialists. The tendency of medicine to pathologise minority cultures is explored through case studies of the approach to rickets and the assessment of health risks associated with consanguineous marriage. Anti-racist approaches have encouraged the consideration of discrimination against and socioeconomic position of minorities. The field has developed with work on nomenclature and the operationalisation of ethnic identity, necessary to study health inequalities between ethnic groups and paying due heed to the contribution of socioeconomic position and racism to group experiences. Research into chronic conditions with complex analysis of a number of distinct contributory variables has been published of late. However, the excessive focus on South Asians and the record of measuring, analysing, but not necessarily tackling health disadvantage, are problems that remain to be addressed

From Monomials to Words to graphs

Given a finite alphabet X and an ordering on the letters, the map \sigma sends each monomial on X to the word that is the ordered product of the letter powers in the monomial. Motivated by a question on Groebner bases, we characterize ideals I in the free commutative monoid (in terms of a generating set) such that the ideal generated by \sigma(I) in the free monoid is finitely generated. Whether there exists an ordering such that is finitely generated turns out to be NP-complete. The latter problem is closely related to the recognition problem for comparability graphs.Comment: 27 pages, 2 postscript figures, uses gastex.st

Priority Downward Closures

When a system sends messages through a lossy channel, then the language encoding all sequences of messages can be abstracted by its downward closure, i.e. the set of all (not necessarily contiguous) subwords. This is useful because even if the system has infinitely many states, its downward closure is a regular language. However, if the channel has congestion control based on priorities assigned to the messages, then we need a finer abstraction: The downward closure with respect to the priority embedding. As for subword-based downward closures, one can also show that these priority downward closures are always regular. While computing finite automata for the subword-based downward closure is well understood, nothing is known in the case of priorities. We initiate the study of this problem and provide algorithms to compute priority downward closures for regular languages, one-counter languages, and context-free languages