A Case Study on Logical Relations using Contextual Types

Proofs by logical relations play a key role to establish rich properties such as normalization or contextual equivalence. They are also challenging to mechanize. In this paper, we describe the completeness proof of algorithmic equality for simply typed lambda-terms by Crary where we reason about logically equivalent terms in the proof environment Beluga. There are three key aspects we rely upon: 1) we encode lambda-terms together with their operational semantics and algorithmic equality using higher-order abstract syntax 2) we directly encode the corresponding logical equivalence of well-typed lambda-terms using recursive types and higher-order functions 3) we exploit Beluga's support for contexts and the equational theory of simultaneous substitutions. This leads to a direct and compact mechanization, demonstrating Beluga's strength at formalizing logical relations proofs.Comment: In Proceedings LFMTP 2015, arXiv:1507.0759

Manipulating the Quota in Weighted Voting Games

Weighted voting games provide a popular model of decision making in multiagent systems. Such games are described by a set of players, a list of players' weights, and a quota; a coalition of the players is said to be winning if the total weight of its members meets or exceeds the quota. The power of a player in such games is traditionally identified with her Shapley--Shubik index or her Banzhaf index, two classical power measures that reflect the player's marginal contributions under different coalition formation scenarios. In this paper, we investigate by how much the central authority can change a player's power, as measured by these indices, by modifying the quota. We provide tight upper and lower bounds on the changes in the individual player's power that can result from a change in quota. We also study how the choice of quota can affect the relative power of the players. From the algorithmic perspective, we provide an efficient algorithm for determining whether there is a value of the quota that makes a given player a {\em dummy}, i.e., reduces his power (as measured by both indices) to 0. On the other hand, we show that checking which of the two values of the quota makes this player more powerful is computationally hard, namely, complete for the complexity class PP, which is believed to be significantly more powerful than NP

Towards Model Checking Real-World Software-Defined Networks (version with appendix)

In software-defined networks (SDN), a controller program is in charge of deploying diverse network functionality across a large number of switches, but this comes at a great risk: deploying buggy controller code could result in network and service disruption and security loopholes. The automatic detection of bugs or, even better, verification of their absence is thus most desirable, yet the size of the network and the complexity of the controller makes this a challenging undertaking. In this paper we propose MOCS, a highly expressive, optimised SDN model that allows capturing subtle real-world bugs, in a reasonable amount of time. This is achieved by (1) analysing the model for possible partial order reductions, (2) statically pre-computing packet equivalence classes and (3) indexing packets and rules that exist in the model. We demonstrate its superiority compared to the state of the art in terms of expressivity, by providing examples of realistic bugs that a prototype implementation of MOCS in UPPAAL caught, and performance/scalability, by running examples on various sizes of network topologies, highlighting the importance of our abstractions and optimisations

Mechanically bonded macromolecules

Mechanically bonded macromolecules constitute a class of challenging synthetic targets in polymer science. The controllable intramolecular motions of mechanical bonds, in combination with the processability and useful physical and mechanical properties of macromolecules, ultimately ensure their potential for applications in materials science, nanotechnology and medicine. This tutorial review describes the syntheses and properties of a library of diverse mechanically bonded macromolecules, which covers (i) main-chain, side-chain, bridged, and pendant oligo/polycatenanes, (ii) main-chain oligo/polyrotaxanes, (iii) poly[c2]daisy chains, and finally (iv) mechanically interlocked dendrimers. A variety of highly efficient synthetic protocols—including template-directed assembly, step-growth polymerisation, quantitative conjugation, etc.—were employed in the construction of these mechanically interlocked architectures. Some of these structures, i.e., side-chain polycatenanes and poly[c2]daisy chains, undergo controllable molecular switching in a manner similar to their small molecular counterparts. The challenges posed by the syntheses of polycatenanes and polyrotaxanes with high molecular weights are contemplated

Symmetry and partial order reduction techniques in model checking Rebeca

Rebeca is an actor-based language with formal semantics that can be used in modeling concurrent and distributed software and protocols. In this paper, we study the application of partial order and symmetry reduction techniques to model checking dynamic Rebeca models. Finding symmetry based equivalence classes of states is in general a difficult problem known to be as hard as graph isomorphism. We show how, for Rebeca models, we can tackle this problem with a polynomial-time solution. Moreover, the coarse-grained interleaving semantics of Rebeca causes considerable reductions when partial order reduction is applied. We have also developed a tool that can make use of both techniques in combination or separately. The evaluation results show significant improvements in model size and model-checking time

3D Supergravity from wrapped D3-branes

AdS_3 solutions dual to N = (0,2) SCFTs arise when D3-branes wrap Kahler two-cycles in manifolds with SU(4) holonomy. Here we review known AdS_3 solutions and identify the corresponding three-dimensional gauged supergravities, solutions of which uplift to type IIB supergravity. In particular, we discuss gauged supergravities dual to twisted compactifications on Riemann surfaces of both N=4 SYM and N =1 SCFTs with Sasaki-Einstein duals. We check in each case that c-extremization gives the exact central charge and R symmetry. For completeness, we also study AdS_3 solutions from intersecting D3-branes, generalise recent KK reductions of Detournay & Guica and identify the underlying gauged supergravities. Finally, we discuss examples of null-warped AdS_3 solutions to three-dimensional gauged supergravity, all of which embed in string theory.Comment: v1 48 pages; v2 two references added, to appear in JHE