Finite Switchboard State Machines Based on Cubic Sets

<p>A commutative cubic fsm <span class="nowrap"><svg height="12.7178pt" id="M141" style="vertical-align:-3.42947pt" version="1.1" viewbox="-0.0498162 -9.28833 76.9392 12.7178" width="76.9392pt" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M896 675C863 652 826 634 783 634C683 634 549 687 439 687C259 687 128 601 128 473C128 383 196 329 279 329C392 329 469 405 496 541H476C440 428 385 359 286 359C224 359 169 400 169 480C169 566 257 641 382 641C475 641 622 584 731 584C796 584 862 620 907 657L896 675ZM658 553C579 484 521 424 454 277C364 81 295 16 184 16C120 16 82 44 78 79H80C87 68 100 67 108 67C136 67 153 89 153 116S131 165 104 165C69 165 43 139 43 91C43 31 110 -15 191 -15C263 -15 321 6 378 45C463 101 526 197 557 304C588 413 618 487 671 539L658 553Z"></path></g><g transform="matrix(.013,0,0,-0.013,15.488,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,26.751,0)"><path d="M360 -163L167 270L360 703H298L106 273V267L298 -163H360Z"></path></g><g transform="matrix(.013,0,0,-0.013,32.12,0)"><path d="M856 669C824 657 796 643 772 628C709 667 631 687 551 687C314 687 158 548 158 412C158 332 216 282 300 282C445 282 516 426 527 561H507C478 406 414 312 302 312C245 312 199 352 199 408C199 535 345 657 550 657C617 657 687 644 742 609C644 538 583 430 495 271C383 71 317 16 193 16C122 16 73 60 73 95H75C82 84 97 83 105 83C133 83 148 106 148 131C148 160 125 179 97 179C64 179 38 151 38 108C38 42 104 -15 211 -15C368 -15 496 71 610 302C672 426 704 522 770 588C803 559 825 518 825 465C825 382 787 316 731 316C710 316 697 328 697 345C697 358 700 380 733 399L723 417C688 398 665 367 665 338C665 303 688 272 737 272C821 272 886 359 886 447C886 516 850 572 797 612C816 627 836 639 863 650L856 669Z"></path></g><g transform="matrix(.013,0,0,-0.013,43.95,0)"><path d="M95 130C70 130 46 113 46 88C46 72 54 64 59 64C93 55 121 33 121 -3C121 -41 93 -68 44 -88L55 -117C117 -98 186 -56 186 22C186 91 131 130 95 130Z"></path></g><g transform="matrix(.013,0,0,-0.013,49.093,0)"><path d="M748 650H522L515 622L546 617C580 611 587 604 565 575C518 513 469 451 419 393C376 474 349 534 330 580C318 609 325 612 361 618L383 622L392 650H151L144 622C214 616 224 612 257 543L360 327C270 218 187 124 159 95C106 40 92 34 26 28L17 0H252L259 28L236 31C189 37 188 47 209 78C249 136 308 210 377 294L478 79C494 44 487 37 449 32L418 28L409 0H673L680 28C596 34 591 39 554 116L436 361C526 469 574 521 604 553C659 612 669 614 739 622L748 650Z"></path></g><g transform="matrix(.013,0,0,-0.013,58.516,0)"><path d="M95 130C70 130 46 113 46 88C46 72 54 64 59 64C93 55 121 33 121 -3C121 -41 93 -68 44 -88L55 -117C117 -98 186 -56 186 22C186 91 131 130 95 130Z"></path></g><g transform="matrix(.013,0,0,-0.013,63.659,0)"><path d="M559 271C559 395 493 448 433 448C370 448 304 394 275 297C259 245 235 121 219 37C157 54 113 110 113 201C113 310 180 386 276 429L265 457C131 410 23 326 23 186C23 83 86 5 211 -10C180 -159 167 -220 158 -252L165 -261C198 -255 236 -246 251 -218L287 -5C421 9 559 119 559 271ZM484 273C484 144 400 40 293 33L352 331C364 389 382 406 405 406C431 406 484 370 484 273Z"></path></g><g transform="matrix(.013,0,0,-0.013,71.226,0)"><path d="M307 267V273L115 703H53L246 270L53 -163H115L307 267Z"></path></g></svg>.</span></p>

Complexity

Finite Switchboard State Machines Based on Cubic Sets

Figure 3