Heaps are well-studied fundamental data structures, having myriads of applications, both theoretical and practical. We consider the problem of designing a heap with an “optimal” extract-min operation. Assuming an arbitrary linear ordering of keys, a heap with n elements typically takes O(log n) time to extract the minimum. Extracting all elements faster is impossible as this would violate the Ω (nlog n) bound for comparison-based sorting. It is known, however, that is takes only O(n+ klog k) time to sort just k smallest elements out of n given, which prompts that there might be a faster heap, whose extract-min performance depends on the number of elements extracted so far. In this paper we show that this is indeed the case. We present a version of heap that performs insert in O(1) time and takes only O(log ∗ n+ log k) time to carry out the k-th extraction (where log ∗ denotes the iterated logarithm). All the above bounds are worst-case. © 2018, Springer Science+Business Media, LLC, part of Springer Nature.
The CCIS series is devoted to the publication of proceedings of computer science conferences. Its aim is to efficiently disseminate original research results in informatics in printed and electronic form. While the focus is on publication of peer-reviewed full papers presenting mature work, inclusion of reviewed short papers reporting on work in progress is welcome, too. Besides globally relevant meetings with internationally representative program committees guaranteeing a strict peer-reviewing and paper selection process, conferences run by societies or of high regional or national relevance are also considered for publication.
The article discusses issues related to computer science and programming teaching for undergraduate students of universities and collegues. Enrollee's classification and expected learning outcomes are included. Every discipline included in Computer Science course is also described in details
The Formal Grammar conference series (FG) provides a forum for the presentation of new and original research on formal grammar, mathematical linguistics, and the application of formal and mathematical methods to the study of natural language. Themes of interest include, but are not limited to: – Formal and computational phonology, morphology, syntax, semantics, and pragmatics – Model-theoretic and proof-theoretic methods in linguistics – Logical aspects of linguistic structure – Constraint-based and resource-sensitive approaches to grammar – Learnability of formal grammar – Integration of stochastic and symbolic models of grammar – Foundational, methodological, and architectural issues in grammar and linguistics – Mathematical foundations of statistical approaches to linguistic analysis Previous FG meetings were held in Barcelona (1995), Prague (1996), Aix-en-Provence (1997), Saarbrücken (1998), Utrecht (1999), Helsinki (2001), Trento (2002), Vienna (2003), Nancy (2004), Edinburgh (2005), Malaga (2006), Dublin (2007), Hamburg (2008), Bordeaux (2009), Copenhagen (2010), Ljubljana (2011), Opole (2012), Düsseldorf (2013), Tübingen (2014), Barcelona (2015), Bolzano-Bozen (2016), and Toulouse (2017). FG 2018, the 23rd conference on Formal Grammar, was held in Sofia, Bulgaria, during August 11–12, 2018. The conference consisted in a special session, dedicated to the memory of Richard T. Oehrle, who passed away in 2018, and seven contributed papers selected from 11 submissions. The present volume includes the contributed papers. We would like to thank the people who made the 23rd FG conference possible: the invited speakers, the members of the Program Committee, and the organizers of ESSLLI 2018, with which the conference was colocated. August 2018 Annie Foret Gerg Kobele Sylvain Pogodalla
Logical frameworks allow the specification of deductive systems using the same logical machinery. Linear logical frameworks have been successfully used for the specification of a number of computational, logics and proof systems. Its success relies on the fact that formulas can be distinguished as linear, which behave intuitively as resources, and unbounded, which behave intuitionistically. Commutative subexponentials enhance the expressiveness of linear logic frameworks by allowing the distinction of multiple contexts. These contexts may behave as multisets of formulas or sets of formulas. Motivated by applications in distributed systems and in type-logical grammar, we propose a linear logical framework containing both commutative and non-commutative subexponentials. Non-commutative subexponentials can be used to specify contexts which behave as lists, not multisets, of formulas. In addition, motivated by our applications in type-logical grammar, where the weakenening rule is disallowed, we investigate the proof theory of formulas that can only contract, but not weaken. In fact, our contraction is non-local. We demonstrate that under some conditions such formulas may be treated as unbounded formulas, which behave intuitionistically.