Congruence from the Operator's Point of View: Compositionality Requirements on Process Semantics

One of the basic sanity properties of a behavioural semantics is that it constitutes a congruence with respect to standard process operators. This issue has been traditionally addressed by the development of rule formats for transition system specifications that define process algebras. In this paper we suggest a novel, orthogonal approach. Namely, we focus on a number of process operators, and for each of them attempt to find the widest possible class of congruences. To this end, we impose restrictions on sublanguages of Hennessy-Milner logic, so that a semantics whose modal characterization satisfies a given criterion is guaranteed to be a congruence with respect to the operator in question. We investigate action prefix, alternative composition, two restriction operators, and parallel composition.Comment: In Proceedings SOS 2010, arXiv:1008.190

On the process of rationalisation of public expenditure

Cele niniejszego artykułu to pełne wyjaśnienie pojęcia racjonalizacji wydatków publicznych, ustalenie różnic między racjonalizacją wyborów a racjonalizacją kosztów, a ponadto ustalenie, czy każde działanie oszczędnościowe można określić mianem racjonalizacji wydatków publicznych. Autor w szczególności przeanalizował zwrot racjonalizacji w kontekście języka prawnego, prawniczego, potocznego i ekonomicznego oraz zaprezentował proces racjonalizacji wydatków publicznych.The aim of this paper is presentation of the term rationalisation of public expenditure, determination of the differences between rationalisation of choices and rationalisation of costs, and furthermore establishment whether each saving act equals to the rationalisation of public expenditure. The author has focused in particular on the analysis of the expression – rationalisation in terms of legal, legalese, colloquial and economic language and present the process of public expenditures rationalisation

Zielonka's Recursive Algorithm: dull, weak and solitaire games and tighter bounds

Dull, weak and nested solitaire games are important classes of parity games, capturing, among others, alternation-free mu-calculus and ECTL* model checking problems. These classes can be solved in polynomial time using dedicated algorithms. We investigate the complexity of Zielonka's Recursive algorithm for solving these special games, showing that the algorithm runs in O(d (n + m)) on weak games, and, somewhat surprisingly, that it requires exponential time to solve dull games and (nested) solitaire games. For the latter classes, we provide a family of games G, allowing us to establish a lower bound of 2^(n/3). We show that an optimisation of Zielonka's algorithm permits solving games from all three classes in polynomial time. Moreover, we show that there is a family of (non-special) games M that permits us to establish a lower bound of 2^(n/3), improving on the previous lower bound for the algorithm.Comment: In Proceedings GandALF 2013, arXiv:1307.416

Strategy Derivation for Small Progress Measures

Small Progress Measures is one of the most efficient parity game solving algorithms. The original algorithm provides the full solution (winning regions and strategies) in $O(dm \cdot (n/\lceil d / 2 \rceil)^{\lceil d/2 \rceil})$ time, and requires a re-run of the algorithm on one of the winning regions. We provide a novel operational interpretation of progress measures, and modify the algorithm so that it derives the winning strategies for both players in one pass. This reduces the upper bound on strategy derivation for SPM to $O(dm \cdot (n/\lfloor d / 2 \rfloor)^{\lfloor d/2 \rfloor})$.Comment: polished the tex

Modal Logic and the Approximation Induction Principle

We prove a compactness theorem in the context of Hennessy-Milner logic. It is used to derive a sufficient condition on modal characterizations for the Approximation Induction Principle to be sound modulo the corresponding process equivalence. We show that this condition is necessary when the equivalence in question is compositional with respect to the projection operators

Expressiveness and Completeness in Abstraction

We study two notions of expressiveness, which have appeared in abstraction theory for model checking, and find them incomparable in general. In particular, we show that according to the most widely used notion, the class of Kripke Modal Transition Systems is strictly less expressive than the class of Generalised Kripke Modal Transition Systems (a generalised variant of Kripke Modal Transition Systems equipped with hypertransitions). Furthermore, we investigate the ability of an abstraction framework to prove a formula with a finite abstract model, a property known as completeness. We address the issue of completeness from a general perspective: the way it depends on certain abstraction parameters, as well as its relationship with expressiveness.Comment: In Proceedings EXPRESS/SOS 2012, arXiv:1208.244

Oink: an Implementation and Evaluation of Modern Parity Game Solvers

Parity games have important practical applications in formal verification and synthesis, especially to solve the model-checking problem of the modal mu-calculus. They are also interesting from the theory perspective, as they are widely believed to admit a polynomial solution, but so far no such algorithm is known. In recent years, a number of new algorithms and improvements to existing algorithms have been proposed. We implement a new and easy to extend tool Oink, which is a high-performance implementation of modern parity game algorithms. We further present a comprehensive empirical evaluation of modern parity game algorithms and solvers, both on real world benchmarks and randomly generated games. Our experiments show that our new tool Oink outperforms the current state-of-the-art.Comment: Accepted at TACAS 201

Impacts of soil conditions and light availability on natural regeneration of Norway spruce Picea abies (L.) H. Karst. in low-elevation mountain forests

& Key message Natural regeneration of P. abies (L.) H. Karst. may reach high densities in lower mountain elevations. The highest densities were found in sites with moderate light availability, with low pH, and not near the riverbank. However, age-height classes differed in the predicted magnitude of response, but were consistent in response directions. Mosses and understory species typical of coniferous forests were positively correlated with regeneration density. & Context Norway spruce Picea abies (L.) H. Karst. in Central Europe is at risk under climate change scenarios, particularly in mountain regions. Little is known about the impact of environmental factors on the natural regeneration of P. abies in lowelevation mountain forests. & Aims We aimed to assess impacts of distance from the riverbank, soil pH, and light availability on natural P. abies regeneration. We hypothesized that (1) natural P. abiesregeneration would depend on light availability and soil pH and (2) there are understory plant species which may indicate the microsites suitable for natural regeneration of P. abies. & Methods The study was conducted in the Stołowe Mountains National Park (SW Poland, 600–800 m a.s.l.). We established 160 study plots (25 m2 ) for natural regeneration, light availability, soil pH, and understory vegetation assessment