Characterisation and macro-modeling of patterned micronic and nano-scale dummy metal-fills in integrated circuits

In this paper, a wideband characterization and macro-modeling of patterned micronic and nano-scale dummy metal-fills is presented. Impacts of patterned dummy metal-fill topologies including square, cross, vertical and horizontal shaped arrays on electrical performances (isolation/coupling, attenuation, guiding properties, etc…) are investigated. The validity of the proposed macro-modeling methodology is demonstrated by comparison with high frequency measurements of dedicated carrier structures including on-chip interconnects and RF inductive loops. An original extraction approach, based on local ground concept, is proposed to capture high frequency behaviour of dummy metal-fill in physics-based compact broadband SPICE model. The RLC parameters are accurately derived using fully scalable closed-form semi-analytical expressions

Tiling solutions for optimal biological sensing

Biological systems, from cells to organisms, must respond to the ever changing environment in order to survive and function. This is not a simple task given the often random nature of the signals they receive, as well as the intrinsically stochastic, many body and often self-organized nature of the processes that control their sensing and response and limited resources. Despite a wide range of scales and functions that can be observed in the living world, some common principles that govern the behavior of biological systems emerge. Here I review two examples of very different biological problems: information transmission in gene regulatory networks and diversity of adaptive immune receptor repertoires that protect us from pathogens. I discuss the trade-offs that physical laws impose on these systems and show that the optimal designs of both immune repertoires and gene regulatory networks display similar discrete tiling structures. These solutions rely on locally non-overlapping placements of the responding elements (genes and receptors) that, overall, cover space nearly uniformly.Comment: 11 page

Infinite games with finite knowledge gaps

Infinite games where several players seek to coordinate under imperfect information are deemed to be undecidable, unless the information is hierarchically ordered among the players. We identify a class of games for which joint winning strategies can be constructed effectively without restricting the direction of information flow. Instead, our condition requires that the players attain common knowledge about the actual state of the game over and over again along every play. We show that it is decidable whether a given game satisfies the condition, and prove tight complexity bounds for the strategy synthesis problem under $\omega$-regular winning conditions given by parity automata.Comment: 39 pages; 2nd revision; submitted to Information and Computatio

Enriched MU-Calculi Module Checking

The model checking problem for open systems has been intensively studied in the literature, for both finite-state (module checking) and infinite-state (pushdown module checking) systems, with respect to Ctl and Ctl*. In this paper, we further investigate this problem with respect to the \mu-calculus enriched with nominals and graded modalities (hybrid graded Mu-calculus), in both the finite-state and infinite-state settings. Using an automata-theoretic approach, we show that hybrid graded \mu-calculus module checking is solvable in exponential time, while hybrid graded \mu-calculus pushdown module checking is solvable in double-exponential time. These results are also tight since they match the known lower bounds for Ctl. We also investigate the module checking problem with respect to the hybrid graded \mu-calculus enriched with inverse programs (Fully enriched \mu-calculus): by showing a reduction from the domino problem, we show its undecidability. We conclude with a short overview of the model checking problem for the Fully enriched Mu-calculus and the fragments obtained by dropping at least one of the additional constructs

Buffered Simulation Games for B\"uchi Automata

Simulation relations are an important tool in automata theory because they provide efficiently computable approximations to language inclusion. In recent years, extensions of ordinary simulations have been studied, for instance multi-pebble and multi-letter simulations which yield better approximations and are still polynomial-time computable. In this paper we study the limitations of approximating language inclusion in this way: we introduce a natural extension of multi-letter simulations called buffered simulations. They are based on a simulation game in which the two players share a FIFO buffer of unbounded size. We consider two variants of these buffered games called continuous and look-ahead simulation which differ in how elements can be removed from the FIFO buffer. We show that look-ahead simulation, the simpler one, is already PSPACE-hard, i.e. computationally as hard as language inclusion itself. Continuous simulation is even EXPTIME-hard. We also provide matching upper bounds for solving these games with infinite state spaces.Comment: In Proceedings AFL 2014, arXiv:1405.527