Using models to model-check recursive schemes

We propose a model-based approach to the model checking problem for recursive schemes. Since simply typed lambda calculus with the fixpoint operator, lambda-Y-calculus, is equivalent to schemes, we propose the use of a model of lambda-Y-calculus to discriminate the terms that satisfy a given property. If a model is finite in every type, this gives a decision procedure. We provide a construction of such a model for every property expressed by automata with trivial acceptance conditions and divergence testing. Such properties pose already interesting challenges for model construction. Moreover, we argue that having models capturing some class of properties has several other virtues in addition to providing decidability of the model-checking problem. As an illustration, we show a very simple construction transforming a scheme to a scheme reflecting a property captured by a given model.Comment: Long version of a paper presented at TLCA 201

Setting up proinnovative networks in Silesia

Silesia is the most industrialized region of Poland recently under huge reindustrialization in an effort to change its heavy industrial pattern into more diversified and innovative one. The reindustrialization processes is additionally complicated by the transformation of Polish economy from central planned to marked oriented. Proinnovative networks, in which under more or less formally conditions cooperate industrial/service companies, research/educational institutions, regional/central governments, professional bodies and even private persons, are put forward as a possible way to solve the reindustrialization problems. Their importance is emphasized in the Regional Development Strategy for Silesia, 2000-2015. The aim of present paper is to study factors and phenomena, which facilitate cooperation of partners within proinnovative networks, as well as describe problems, which are, faced both when setting up such a network and in its day by day business. Special attention is paid to so-called soft factors, the social capital of partners cooperating in the network. We introduce certain measures of social capital and demonstrate their usefulness. In second part of the paper we present a number of case studies of Silesia proinnovative networks. For each network we describe its objective, short history with results achieved so far, and future plans. We pay special attention to these networks, which are considered, at least in part, as the results of projects under the Framework Programmes of European Union.

Institutional settings for networking in Poland

We consider institutional settings for networking in the context of innovative regional strategy development. Several examples of such institutions will be given and then conclusions and recommendations will be formulated emphasizing the pre-accession context. Poland completed the comprehensive reform of regional and local administration to have achieved a system similar to the system existing in the European Union. The system is based on the NUTS 2 size regions. Therefore, the competencies of the state and regional authorities to develop S/TD and Innovation infrastructure and policies in Poland are appropriate to the standards in the European Union. The paper will start with critical evaluation of the regional development policies recently presented by the regional self-governments in Poland. The overview of the implementation measures for these policies will be presented with an emphasis put on the pre-accession context. The second part of the contribution gives assumptions and general description of the Poland's National and Regional Innovation Systems that is substantially based on the findings of the Phare SCI-TECH II Programme concluded in 2000. The Centre for Industrial Management PAS took an active role in the implementation of this Programme. The analysis is based on the so-called 'Learning Regions', in which the role of dense inter-connetions between segments in the innovation systems comes into prominence.

Static Analysis of Deterministic Negotiations

Negotiation diagrams are a model of concurrent computation akin to workflow Petri nets. Deterministic negotiation diagrams, equivalent to the much studied and used free-choice workflow Petri nets, are surprisingly amenable to verification. Soundness (a property close to deadlock-freedom) can be decided in PTIME. Further, other fundamental questions like computing summaries or the expected cost, can also be solved in PTIME for sound deterministic negotiation diagrams, while they are PSPACE-complete in the general case. In this paper we generalize and explain these results. We extend the classical "meet-over-all-paths" (MOP) formulation of static analysis problems to our concurrent setting, and introduce Mazurkiewicz-invariant analysis problems, which encompass the questions above and new ones. We show that any Mazurkiewicz-invariant analysis problem can be solved in PTIME for sound deterministic negotiations whenever it is in PTIME for sequential flow-graphs---even though the flow-graph of a deterministic negotiation diagram can be exponentially larger than the diagram itself. This gives a common explanation to the low-complexity of all the analysis questions studied so far. Finally, we show that classical gen/kill analyses are also an instance of our framework, and obtain a PTIME algorithm for detecting anti-patterns in free-choice workflow Petri nets. Our result is based on a novel decomposition theorem, of independent interest, showing that sound deterministic negotiation diagrams can be hierarchically decomposed into (possibly overlapping) smaller sound diagrams.Comment: To appear in the Proceedings of LICS 2017, IEEE Computer Societ

Positional Determinacy of Games with Infinitely Many Priorities

We study two-player games of infinite duration that are played on finite or infinite game graphs. A winning strategy for such a game is positional if it only depends on the current position, and not on the history of the play. A game is positionally determined if, from each position, one of the two players has a positional winning strategy. The theory of such games is well studied for winning conditions that are defined in terms of a mapping that assigns to each position a priority from a finite set. Specifically, in Muller games the winner of a play is determined by the set of those priorities that have been seen infinitely often; an important special case are parity games where the least (or greatest) priority occurring infinitely often determines the winner. It is well-known that parity games are positionally determined whereas Muller games are determined via finite-memory strategies. In this paper, we extend this theory to the case of games with infinitely many priorities. Such games arise in several application areas, for instance in pushdown games with winning conditions depending on stack contents. For parity games there are several generalisations to the case of infinitely many priorities. While max-parity games over omega or min-parity games over larger ordinals than omega require strategies with infinite memory, we can prove that min-parity games with priorities in omega are positionally determined. Indeed, it turns out that the min-parity condition over omega is the only infinitary Muller condition that guarantees positional determinacy on all game graphs

Weak Alternating Timed Automata

Alternating timed automata on infinite words are considered. The main result is a characterization of acceptance conditions for which the emptiness problem for these automata is decidable. This result implies new decidability results for fragments of timed temporal logics. It is also shown that, unlike for MITL, the characterisation remains the same even if no punctual constraints are allowed

Consistency and Completeness of Rewriting in the Calculus of Constructions

Adding rewriting to a proof assistant based on the Curry-Howard isomorphism, such as Coq, may greatly improve usability of the tool. Unfortunately adding an arbitrary set of rewrite rules may render the underlying formal system undecidable and inconsistent. While ways to ensure termination and confluence, and hence decidability of type-checking, have already been studied to some extent, logical consistency has got little attention so far. In this paper we show that consistency is a consequence of canonicity, which in turn follows from the assumption that all functions defined by rewrite rules are complete. We provide a sound and terminating, but necessarily incomplete algorithm to verify this property. The algorithm accepts all definitions that follow dependent pattern matching schemes presented by Coquand and studied by McBride in his PhD thesis. It also accepts many definitions by rewriting, containing rules which depart from standard pattern matching.Comment: 20 page