Formal Verification of Hardware Components in Critical Systems

<table class="algorithm-group"><tr><td><table class="algorithm" id="alg7"><tr><td>(1)</td><td>Definition F(x y: bool) : circuit <svg height="5.81497pt" id="M39" style="vertical-align:-0.2063899pt" version="1.1" viewbox="-0.0498162 -5.60858 10.7344 5.81497" width="10.7344pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M116 412C83 412 59 388 59 355C59 321 83 297 115 297S170 321 170 355C170 388 147 412 116 412ZM114 -12C147 -12 171 11 171 46C171 78 147 103 115 103C84 103 60 78 60 46C60 11 84 -12 114 -12Z"></path></g><g transform="matrix(.013,0,0,-0.013,2.964,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g></svg> <svg height="5.65839pt" id="M40" style="vertical-align:-0.04980993pt" version="1.1" viewbox="-0.0498162 -5.60858 8.02023 5.65839" width="8.02023pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M554 94V368H71V318H496V94H554Z"></path></g></svg>x<svg height="6.01072pt" id="M41" style="vertical-align:-0.04980993pt" version="1.1" viewbox="-0.0498162 -5.96091 7.75925 6.01072" width="7.75925pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M471 153C471 170 463 194 452 212C400 220 373 229 322 255C373 281 400 290 452 298C463 316 471 339 471 357C456 366 431 371 410 370C377 329 356 310 308 279C311 336 317 364 336 413C326 432 310 451 294 459C279 451 262 432 252 413C271 364 277 336 280 279C232 310 211 329 178 370C157 371 132 367 117 357C117 340 125 316 136 298C188 290 215 281 266 255C215 229 188 220 136 212C125 194 117 171 117 153C132 144 157 139 178 140C211 181 232 200 280 231C277 174 271 146 252 97C262 78 278 59 294 51C309 59 326 78 336 97C317 146 311 174 308 231C356 200 377 181 410 140C431 139 456 143 471 153Z"></path></g></svg><svg height="5.65839pt" id="M42" style="vertical-align:-0.04980993pt" version="1.1" viewbox="-0.0498162 -5.60858 8.02023 5.65839" width="8.02023pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M554 94V368H71V318H496V94H554Z"></path></g></svg>y::nil.</td></tr></table></td></tr></table>

<div> Example of circuit description in Coq notations.</div>

Wireless Communications and Mobile Computing

alg7

Listing 7

Listing 7: Formal Verification of Hardware Components in Critical Systems 