Strengthening Model Checking Techniques with Inductive Invariants

This paper describes optimized techniques to efficiently compute and reap benefits from inductive invariants within SAT-based model checking. We address sequential circuit verification, and we consider both equivalences and implications between pairs of nodes in the logic networks. First, we present a very efficient dynamic procedure, based on equivalence classes and incremental SAT, specifically oriented to reduce the set of checked invariants. Then, we show how to effectively integrate the computation of inductive invariants within state-of-the-art SAT-based model checking procedures. Experiments (on more than 600 designs) show the robustness of our approach on verification instances on which stand-alone techniques fai

On the Rationality of Escalation

Escalation is a typical feature of infinite games. Therefore tools conceived for studying infinite mathematical structures, namely those deriving from coinduction are essential. Here we use coinduction, or backward coinduction (to show its connection with the same concept for finite games) to study carefully and formally the infinite games especially those called dollar auctions, which are considered as the paradigm of escalation. Unlike what is commonly admitted, we show that, provided one assumes that the other agent will always stop, bidding is rational, because it results in a subgame perfect equilibrium. We show that this is not the only rational strategy profile (the only subgame perfect equilibrium). Indeed if an agent stops and will stop at every step, we claim that he is rational as well, if one admits that his opponent will never stop, because this corresponds to a subgame perfect equilibrium. Amazingly, in the infinite dollar auction game, the behavior in which both agents stop at each step is not a Nash equilibrium, hence is not a subgame perfect equilibrium, hence is not rational.Comment: 19 p. This paper is a duplicate of arXiv:1004.525

Magnetic Cellular Nonlinear Network with Spin Wave Bus for Image Processing

We describe and analyze a cellular nonlinear network based on magnetic nanostructures for image processing. The network consists of magneto-electric cells integrated onto a common ferromagnetic film - spin wave bus. The magneto-electric cell is an artificial two-phase multiferroic structure comprising piezoelectric and ferromagnetic materials. A bit of information is assigned to the cell's magnetic polarization, which can be controlled by the applied voltage. The information exchange among the cells is via the spin waves propagating in the spin wave bus. Each cell changes its state as a combined effect of two: the magneto-electric coupling and the interaction with the spin waves. The distinct feature of the network with spin wave bus is the ability to control the inter-cell communication by an external global parameter - magnetic field. The latter makes possible to realize different image processing functions on the same template without rewiring or reconfiguration. We present the results of numerical simulations illustrating image filtering, erosion, dilation, horizontal and vertical line detection, inversion and edge detection accomplished on one template by the proper choice of the strength and direction of the external magnetic field. We also present numerical assets on the major network parameters such as cell density, power dissipation and functional throughput, and compare them with the parameters projected for other nano-architectures such as CMOL-CrossNet, Quantum Dot Cellular Automata, and Quantum Dot Image Processor. Potentially, the utilization of spin waves phenomena at the nanometer scale may provide a route to low-power consuming and functional logic circuits for special task data processing

Interacting Hopf Algebras

We introduce the theory IH of interacting Hopf algebras, parametrised over a principal ideal domain R. The axioms of IH are derived using Lack's approach to composing PROPs: they feature two Hopf algebra and two Frobenius algebra structures on four different monoid-comonoid pairs. This construction is instrumental in showing that IH is isomorphic to the PROP of linear relations (i.e. subspaces) over the field of fractions of R

Fault Tolerance in Cellular Automata at High Fault Rates

A commonly used model for fault-tolerant computation is that of cellular automata. The essential difficulty of fault-tolerant computation is present in the special case of simply remembering a bit in the presence of faults, and that is the case we treat in this paper. We are concerned with the degree (the number of neighboring cells on which the state transition function depends) needed to achieve fault tolerance when the fault rate is high (nearly 1/2). We consider both the traditional transient fault model (where faults occur independently in time and space) and a recently introduced combined fault model which also includes manufacturing faults (which occur independently in space, but which affect cells for all time). We also consider both a purely probabilistic fault model (in which the states of cells are perturbed at exactly the fault rate) and an adversarial model (in which the occurrence of a fault gives control of the state to an omniscient adversary). We show that there are cellular automata that can tolerate a fault rate $1/2 - \xi$ (with $\xi>0$) with degree $O((1/\xi^2)\log(1/\xi))$, even with adversarial combined faults. The simplest such automata are based on infinite regular trees, but our results also apply to other structures (such as hyperbolic tessellations) that contain infinite regular trees. We also obtain a lower bound of $\Omega(1/\xi^2)$, even with purely probabilistic transient faults only