Meta-Kernelization with Structural Parameters

Meta-kernelization theorems are general results that provide polynomial kernels for large classes of parameterized problems. The known meta-kernelization theorems, in particular the results of Bodlaender et al. (FOCS'09) and of Fomin et al. (FOCS'10), apply to optimization problems parameterized by solution size. We present the first meta-kernelization theorems that use a structural parameters of the input and not the solution size. Let C be a graph class. We define the C-cover number of a graph to be a the smallest number of modules the vertex set can be partitioned into, such that each module induces a subgraph that belongs to the class C. We show that each graph problem that can be expressed in Monadic Second Order (MSO) logic has a polynomial kernel with a linear number of vertices when parameterized by the C-cover number for any fixed class C of bounded rank-width (or equivalently, of bounded clique-width, or bounded Boolean width). Many graph problems such as Independent Dominating Set, c-Coloring, and c-Domatic Number are covered by this meta-kernelization result. Our second result applies to MSO expressible optimization problems, such as Minimum Vertex Cover, Minimum Dominating Set, and Maximum Clique. We show that these problems admit a polynomial annotated kernel with a linear number of vertices

An algebraic basis for specifying and enforcing access control in security systems

Security services in a multi-user environment are often based on access control mechanisms. Static aspects of an access control policy can be formalised using abstract algebraic models. We integrate these static aspects into a dynamic framework considering requesting access to resources as a process aiming at the prevention of access control violations when a program is executed. We use another algebraic technique, monads, as a meta-language to integrate access control operations into a functional programming language. The integration of monads and concepts from a denotational model for process algebras provides a framework for programming of access control in security systems

A Proof Strategy Language and Proof Script Generation for Isabelle/HOL

We introduce a language, PSL, designed to capture high level proof strategies in Isabelle/HOL. Given a strategy and a proof obligation, PSL's runtime system generates and combines various tactics to explore a large search space with low memory usage. Upon success, PSL generates an efficient proof script, which bypasses a large part of the proof search. We also present PSL's monadic interpreter to show that the underlying idea of PSL is transferable to other ITPs.Comment: This paper has been submitted to CADE2

Modularity in Meta-Languages

A meta-language for semantics has a high degree of modularitywhen descriptions of individual language constructs can be formulated independently using it, and do not require reformulation when new constructs are added to the described language. The quest for modularity in semantic meta-languages has been going on for more than two decades. Here, most of the main meta-languages for operational, denotational, and hybrid styles of semantics are compared regarding their modularity. A simple bench-mark is used: describing the semantics of a pure functional language, then extending the described language with references, exceptions, and concurrency constructs. For each style of semantics, at least one of the considered meta-languages appears to provide a high degree of modularity

Logics of Finite Hankel Rank

We discuss the Feferman-Vaught Theorem in the setting of abstract model theory for finite structures. We look at sum-like and product-like binary operations on finite structures and their Hankel matrices. We show the connection between Hankel matrices and the Feferman-Vaught Theorem. The largest logic known to satisfy a Feferman-Vaught Theorem for product-like operations is CFOL, first order logic with modular counting quantifiers. For sum-like operations it is CMSOL, the corresponding monadic second order logic. We discuss whether there are maximal logics satisfying Feferman-Vaught Theorems for finite structures.Comment: Appeared in YuriFest 2015, held in honor of Yuri Gurevich's 75th birthday. The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-23534-9_1

Modal logics are coalgebraic

Applications of modal logics are abundant in computer science, and a large number of structurally different modal logics have been successfully employed in a diverse spectrum of application contexts. Coalgebraic semantics, on the other hand, provides a uniform and encompassing view on the large variety of specific logics used in particular domains. The coalgebraic approach is generic and compositional: tools and techniques simultaneously apply to a large class of application areas and can moreover be combined in a modular way. In particular, this facilitates a pick-and-choose approach to domain specific formalisms, applicable across the entire scope of application areas, leading to generic software tools that are easier to design, to implement, and to maintain. This paper substantiates the authors' firm belief that the systematic exploitation of the coalgebraic nature of modal logic will not only have impact on the field of modal logic itself but also lead to significant progress in a number of areas within computer science, such as knowledge representation and concurrency/mobility