Complexity of Maximum Cut on Interval Graphs

We resolve the longstanding open problem concerning the computational complexity of Max Cut on interval graphs by showing that it is NP-complete

Complexity and Approximability of Parameterized MAX-CSPs

International audienceWe study the optimization version of constraint satisfaction problems (Max-CSPs) in the framework of parameterized complexity; the goal is to compute the maximum fraction of constraints that can be satisfied simultaneously. In standard CSPs, we want to decide whether this fraction equals one. The parameters we investigate are structural measures, such as the treewidth or the clique-width of the variable-constraint incidence graph of the CSP instance.We consider Max-CSPs with the constraint types AND, OR, PARITY, and MAJORITY, and with various parameters k, and we attempt to fully classify them into the following three cases: 1. The exact optimum can be computed in FPT time. 2. It is W[1]-hard to compute the exact optimum, but there is a randomized FPT approximation scheme (FPTAS), which computes a (1−ϵ)-approximation in time f(k,ϵ)⋅poly(n). 3. There is no FPTAS unless FPT=W[1].For the corresponding standard CSPs, we establish FPT vs. W[1]-hardness results

Partial words and the critical factorization theorem revisited

In this paper, we consider one of the most fundamental results on the periodicity of words, namely the critical factorization theorem. Given a word w and nonempty words u, v satisfying w = uv, the minimal local period associated with the factorization (u, v) is the length of the shortest square at position |u| - 1. The critical factorization theorem shows that for any word, there is always a factorization whose minimal local period is equal to the minimal period (or global period) of the word. Crochemore and Perrin presented a linear time algorithm (in the length of the word) that finds a critical factorization from the computation of the maximal suffixes of the word with respect to two total orderings on words: the lexicographic ordering related to a fixed total ordering on the alphabet, and the lexicographic ordering obtained by reversing the order of letters in the alphabet. Here, by refining Crochemore and Perrin’s algorithm, we give a version of the critical factorization theorem for partial words (such sequences may contain ?do not know? symbols or ?holes?). Our proof provides an efficient algorithm which computes a critical factorization when one exists. Our results extend those of Blanchet-Sadri and Duncan for partial words with one hole. A World Wide Web server interface at http://www.uncg.edu/mat/research/cft2/ has been established for automated use of the program

Hienojakoiset staattiset pääsyrajoitteet Java-ohjelmien osien eristyneisyyden takaajina

Java-kielessä ohjelmaelementti voi olla saatavissa kaikkialla, vain aliluokissa sekä esittelevässä pakkauksessa, vain esittelevässä pakkauksessa tai vain esittelevässä luokassa. Saatavuustasojen jaottelua voidaan pitää karkeana. On olemassa tapauksia, joissa ohjelmaelementin saatavuuden täytyy olla laajempi kuin saatavuuden todellinen tarve vaatisi. Seurauksena abstraktioiden sisäiset toteutusyksityiskohdat ovat näkyvissä laajemmalle kuin on tarpeen, mikä yleensä johtaa ohjelman sisäisten riippuvuuksien lisääntymiseen heikentäen sen modulaarisuutta. Optimaalisen saatavuuden mahdollistamiseksi esitän ratkaisuksi kytkettävää pääsynvalvontaa. Se soveltaa kytkettävien tyyppijärjestelmien ideaa pääsynvalvontaan. Kytkettävä tyyppijärjestelmä on ohjelmointikielestä erillinen staattinen tyyppijärjestelmä, jonka toteutus on kytkettävissä tarpeen mukaan ohjelmointikieleen valinnaisena laajennoksena. Tutkielmassa esitän suunnitelmat kytkettävästä pääsynvalvontajärjestelmästä pääsymääreineen sekä kytkettävän pääsynvalvontakehyksen toteutuksesta Javalle. Osoitan kytkettävän pääsynvalvonnan mahdollistavan optimaalisen saatavuuden soveltamalla suunnittelemaani pääsynvalvontajärjestelmää tapauksiin, joissa Javan pääsynvalvontajärjestelmä osoittautuu karkeaksi. Kytkettävän pääsynvalvontakehyksen suunnitelman pohjalta rakennettu prototyyppi osoittaa ratkaisun olevan käytännössä toteutettavissa. Suunnitellut pääsymääreet hyödyntävät monipuolisesti erilaisia saatavuusperusteita. Yksinkertaisen perusarkkitehtuurin ansiosta eri pääsymääreiden yhteiskäyttö on ongelmatonta. Kytkettävä pääsynvalvonta osoittautuu ilmaisuvoimaiseksi ja valinnaisuutensa ansiosta joustavaksi välineeksi täydentämään ohjelmointikielen omaa pääsynvalvontaa

Higher-Order Subtyping with Type Intervals

Modern, statically typed programming languages provide various abstraction facilities at both the term- and type-level. Common abstraction mechanisms for types include parametric polymorphism -- a hallmark of functional languages -- and subtyping -- which is pervasive in object-oriented languages. Additionally, both kinds of languages may allow parametrized (or generic) datatype definitions in modules or classes. When several of these features are present in the same language, new and more expressive combinations arise, such as (1) bounded quantification, (2) bounded operator abstractions and (3) translucent type definitions. An example of such a language is Scala, which features all three of the aforementioned type-level constructs. This increases the expressivity of the language, but also the complexity of its type system. From a theoretical point of view, the various abstraction mechanisms have been studied through different extensions of Girard's higher-order polymorphic lambda-calculus F-omega. Higher-order subtyping and bounded polymorphism (1 and 2) have been formalized in F-omega-sub and its many variants; type definitions of various degrees of opacity (3) have been formalized through extensions of F-omega with singleton types. In this dissertation, I propose type intervals as a unifying concept for expressing (1--3) and other related constructs. In particular, I develop an extension of F-omega with interval kinds as a formal theory of higher-order subtyping with type intervals, and show how the familiar concepts of higher-order bounded quantification, bounded operator abstraction and singleton kinds can all be encoded in a semantics-preserving way using interval kinds. Going beyond the status quo, the theory is expressive enough to also cover less familiar constructs, such as lower-bounded operator abstractions and first-class, higher-order inequality constraints. I establish basic metatheoretic properties of the theory: I prove that subject reduction holds for well-kinded types w.r.t. full beta-reduction, that types and kinds are weakly normalizing, and that the theory is type safe w.r.t. its call-by-value operational reduction semantics. Key to this metatheoretic development is the use of hereditary substitution and the definition of an equivalent, canonical presentation of subtyping, which involves only normal types and kinds. The resulting metatheory is entirely syntactic, i.e. does not involve any model constructions, and has been fully mechanized in Agda. The extension of F-omega with interval kinds constitutes a stepping stone to the development of a higher-order version of the calculus of Dependent Object Types (DOT) -- the theoretical foundation of Scala's type system. In the last part of this dissertation, I briefly sketch a possible extension of the theory toward this goal and discuss some of the challenges involved in adapting the existing metatheory to that extension