TY - CONF
AB - A controller is an environment for a system that achieves a particular control objective by providing inputs to the system without constraining the choices of the system. For synchronous systems, where system and controller make simultaneous and interdependent choices, the notion that a controller must not constrain the choices of the system can be formalized by type systems for composability. In a previous paper, we solved the control problem for static and dynamic types: a static type is a dependency relation between inputs and outputs, and composition is well-typed if it does not introduce cyclic dependencies; a dynamic type is a set of static types, one for each state. Static and dynamic types, however, cannot capture many important digital circuits, such as gated clocks, bidirectional buses, and random-access memory. We therefore introduce more general type systems, so-called dependent and bidirectional types, for modeling these situations, and we solve the corresponding control problems.
In a system with a dependent type, the dependencies between inputs and outputs are determined gradually through a game of the system against the controller. In a system with a bidirectional type, also the distinction between inputs and outputs is resolved dynamically by such a game. The game proceeds in several rounds. In each round the system and the controller choose to update some variables dependent on variables that have already been updated. The solution of the control problem for dependent and bidirectional types is based on algorithms for solving these games.
AU - de Alfaro, Luca
AU - Thomas Henzinger
AU - Mang, Freddy Y
ID - 4634
TI - The control of synchronous systems, Part II
VL - 2154
ER -
TY - CONF
AB - We show how model checking techniques can be applied to the analysis of connectivity and cost-of-traversal properties of Web sites.
AU - de Alfaro, Luca
AU - Thomas Henzinger
AU - Mang, Freddy Y
ID - 4635
TI - MCWEB: A model-checking tool for web-site debugging
ER -
TY - CONF
AB - Abstract. Dynamic programs, or fixpoint iteration schemes, are useful for solving many problems on state spaces, including model checking on Kripke structures (“verification”), computing shortest paths on weighted graphs (“optimization”), computing the value of games played on game graphs (“control”). For Kripke structures, a rich fixpoint theory is available in the form of the µ-calculus. Yet few connections have been made between different interpretations of fixpoint algorithms. We study the question of when a particular fixpoint iteration scheme ϕ for verifying an ω-regular property Ψ on a Kripke structure can be used also for solving a two-player game on a game graph with winning objective Ψ. We provide a sufficient and necessary criterion for the answer to be affirmative in the form of an extremal-model theorem for games: under a game interpretation, the dynamic program ϕ solves the game with objective Ψ if and only if both (1) under an existential interpretation on Kripke structures, ϕ is equivalent to ∃Ψ, and (2) under a universal interpretation on Kripke structures, ϕ is equivalent to ∀Ψ. In other words, ϕ is correct on all two-player game graphs iff it is correct on all extremal game graphs, where one or the other player has no choice of moves. The theorem generalizes to quantitative interpretations, where it connects two-player games with costs to weighted graphs. While the standard translations from ω-regular properties to the µ-calculus violate (1) or (2), we give a translation that satisfies both conditions. Our construction, therefore, yields fixpoint iteration schemes that can be uniformly applied on Kripke structures, weighted graphs, game graphs, and game graphs with costs, in order to meet or optimize a given ω-regular objective.
AU - de Alfaro, Luca
AU - Thomas Henzinger
AU - Majumdar, Ritankar S
ID - 4636
TI - From verification to control: dynamic programs for omega-regular objectives
ER -
TY - JOUR
AB - In this Note we present pairs of hyperkähler orbifolds which satisfy two different versions of mirror symmetry. On the one hand, we show that their Hodge numbers (or more precisely, stringy E-polynomials) are equal. On the other hand, we show that they satisfy the prescription of Strominger, Yau, and Zaslow (which in the present case goes back to Bershadsky, Johansen, Sadov and Vafa): that a Calabi-Yau and its mirror should fiber over the same real manifold, with special Lagrangian fibers which are tori dual to each other. Our examples arise as moduli spaces of local systems on a curve with structure group SL(n); the mirror is the corresponding space with structure group PGL(n). The special Lagrangian tori come from an algebraically completely integrable Hamiltonian system: the Hitchin system.
AU - Tamas Hausel
AU - Thaddeus, Michael
ID - 1452
IS - 4
JF - Comptes Rendus de l'Academie des Sciences - Series I: Mathematics
TI - Examples of mirror partners arising from integrable systems
VL - 333
ER -
TY - JOUR
AB - In this Letter we exhibit a one-parameter family of new Taub-NUT instantons parameterized by a half-line. The endpoint of the half-line will be the reducible Yang-Mills instanton corresponding to the Eguchi-Hanson-Gibbons L2 harmonic 2-form, while at an inner point we recover the Pope-Yuille instanton constructed as a projection of the Levi-Civitá connection onto the positive su(2)+ ⊂ so(4) subalgebra. Our method imitates the Jackiw-Nohl-Rebbi construction originally designed for flat R4. That is we find a one-parameter family of harmonic functions on the Taub-NUT space with a point singularity, rescale the metric and project the obtained Levi-Civitá connection onto the other negative su(2)- ⊂ so(4) part. Our solutions will possess the full U(2) symmetry, and thus provide more solutions to the recently proposed U(2) symmetric ansatz of Kim and Yoon.
AU - Etesi, Gábor
AU - Tamas Hausel
ID - 1453
IS - 1-2
JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
TI - Geometric construction of new Yang-Mills instantons over Taub-NUT space
VL - 514
ER -