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In a previous paper, we have shown that any Boolean formula can be encoded as a linear programming problem in the framework of Bayesian probability theory. When applied to NP-complete algorithms, this leads to the fundamental conclusion that P = NP. Now, we implement this concept in elementary arithmetic and especially in multiplication. This provides a polynomial time deterministic factoring algorithm, while no such algorithm is known to day. This result clearly appeals for a revaluation of the current cryptosystems. The Bayesian arithmetic environment can also be regarded as a toy model for quantum mechanics.

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Nonlinear interactions between noncollinear ASW with exact phase matching provide a special kind of convolution and correlation, according to the ratio ω1/ω2 of the input frequencies. It means that the time scale at the output port depending on this ratio, time compression or expansion can be achieved. The same device can be used for both correlation and convolution with equal NL conversion efficiency.

SAW voltage-controlled oscillators are very easily implemented using a conventional hybrid junction and varactors. Taking advantage of this, a similar device may be designed for use as an electrically tunable filter. The device consists of a SAW delay line w i t h moderate insertion loss and closed through a low-noise amplifier i n order t o maintain the loop losses t o a few dB. In addition, a phase-shifter is inserted in the loop t o match the overall phase. The input is typically the input of the amplifier, while the output may be similarly the output of the amplifier, for l o w loss, or an auxiliary SAW transducer designed t o compensate for the frequency response o f the delay line. This is a very agile narrow bandwidth f i l t e r w i t h the capability of meeting the requirements of the future vehicular communication system w i t h frequency around 900 MHZ.This type of tunable SAW f i l t e r has been f i r s t implemented at about 200 M H Z on lithium tantalate and experimental results are reported. I -IntroductionThe development of future vehicular communicat i o n system requires the use of agile narrow bandwidth filters : the bandwidth is typically a few tens of kilohertz but the carrier frequency is tentatively fixed around 900 MHz. The conventional solution is t o use a frequency conversion t o obtain a fixed intermediate frequency and then the main problem consists in tuning very rapidly (in a few milliseconds) the frequency of the down frequency converter. In addition, since many adjacent channels (typically 1000) are available the second drastic problem is t o secure a good immunity against intermodulation. In this paper we suggest t o design an electrically tunable narrow-bandwidth in-frontfilter, directly at the carrier frequency. This obviates both shorthcomings of the conventional solution. I1 -Principle of electrically tunable f i l t e rThe device is built as a tunable SAW oscillator [1,2] (cf. Fig. 1). A SAW delay line is inserted in a closed loop together w i t h an amplifier and a phase shifter. If the gain of the amplifier increases up t o compensate for the loss, the device is indeed an oscillator operating at a frequency w0 defined by where 0 is the auxiliary p%ase shift, T the delay of the SAW line and k is an integer. F r o m the wellknown design rules of such an oscillator, the transducer lengths are chosen i n order t o have a single mode operation. If, next, the gain o f the amplifier decreases leading t o a linear closed loop gain r less than unity, the transfer @I+ U T = 2 k n AV, 1 T AV2 Fig.1. : Schematic o f the electrically tunable f i Zt e r . function f r o m the input t o the output is roughly : 1 3 1 -2 1 + 2jQ (-) 0 0 2 k n -@ T where Q =a=& and W O = (k is the effective number of wavelengths in the delayline accounting for both electrical and mechanical reflections). The voltage-controlled phase-shifter PS is conveniently realized using a quadrature hybrid junction and varactors : this leads t o a very agile tuning of the filter, especially at the high frequency of o...

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A B Michel FELDMANN, J e a n n i n e HENAFF and Marie-Ange KIROV Angles Cut Prop. v e l o c i t y coupl.coei'. v m/s k 2 I cy 8 XYZ XYZ CO Ex CO Ex 90" 45" 0 001 110 2863 0.09 --o 450 5407 111 iio 2426 2432 8 10-5 -CNET -P a r i s B 196 Rue d e P a r i s , 92220 BAGNEUX, FRANCE.C 0 A b s t r a c t