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E e E e 0 E Some remarks on ! 2 e 00 E ! 2 e 00 E w equivalence of graph-to-graph transducers inc( w, e 0 ) inc( w, e 00 ) Schmude, J. Boja czyk, M. University of Warsaw Highlights of Logic,

  1. ∃ E e ∈ E ∧ ∀ e 0 ∈ E Some remarks on ∃ ! 2 e 00 ∈ E ∧ ∃ ! 2 e 00 ∈ E ∃ w equivalence of graph-to-graph transducers inc( w, e 0 ) ∧ inc( w, e 00 ) Schmude, J. Boja ń czyk, M. University of Warsaw Highlights of Logic, Games and Automata 2020, September 15-18

  2. <latexit sha1_base64="uWCbEYn82afSBWJvipScetRC9VA=">ACGnicbVC7SgNBFJ2NrxhfUubxSBYhV2JaBm0sYxgHpAs4c7sJBky+3DmrCEfIeNhf6Kndja+CeWziZbmMQDA4dz7p17ODSWQqPjfFuFtfWNza3idmlnd2/oHx41NJRohvskhGqkNBcylC3kSBkndixSGgkrfp+Dbz209caRGFD5jG3AtgGIqBYIBG8igAUKA96Ueo+WKU3VmsFeJm5MKydHol396fsSgIfIJGjdZ0YvQkoFEzyamXaB4DG8OQdw0NIeDam8xCT+0zo/j2IFLmhWjP1L8bEwi0TgNqJgPAkV72MvE/r5vg4NqbiDBOkIdsfmiQSBsjO2vA9oXiDGVqCDAlTFabjUABQ9PTwhWNAahU+eaPLGdPSmrGxhxLpip3uZhV0rqourXq5X2tUr/JSyuSE3JKzolLrkid3JEGaRJGHskzeSVv1ov1bn1Yn/PRgpXvHJMFWF+/sC2hvQ=</latexit> <latexit sha1_base64="5vep7nCbjRhZ5rEQN9s1cI/sZFE=">ACGHicbVC7SgNBFJ2NrxhfUubwSBYhV1RtAzaWEYwD9iEcHd2Nhkyu7PM3BVCyGfYWOiv2ImtnX9i6STZwiQeGDic+zpzglQKg67RTW1jc2t4rbpZ3dvf2D8uFR06hM95gSirdDsBwKRLeQIGSt1PNIQ4kbwXDu2m9cS1ESp5xFHKuzH0ExEJBmglH4IAoCNDhaZXrhVdwa6SrycVEiOeq/80wkVy2KeIJNgjO+5KXbHoFEwySelTmZ4CmwIfe5bmkDMTXc8szyhZ1YJaS0fQnSmfp3YgyxMaM4sJ0x4MAs16bifzU/w+imOxZJmiFP2PxQlEmKik7/T0OhOUM5sgSYFtYrZQPQwNCmtHDFYAx6pEO7Y+qzI2Vg24YcSzYqbzmYVdK8qHqX1auHy0rtNg+tSE7IKTknHrkmNXJP6qRBGFHkmbySN+fFeXc+nM95a8HJZ47JApyvXxioOY=</latexit> <latexit sha1_base64="goaEZfstFv1SxfyiQGmTzJCr1Q=">ACL3icbZC7SgNBFIZn4y3GW9TSZjAIVmFXFC2DNpYRzAWSJZyZnSRDZi/MnBXCktansbHQVxEbsfUNLJ1cQJN4YODjP9f5WaKkQd9d3Irq2vrG/nNwtb2zu5ecf+gbuJUc1HjsYp1k4ERSkaihKVaCZaQMiUaLDBzTjfeBDayDi6x2Ei/B6kexKDmilTpEyYG0VxGgo+0UAxuiUO8WSW3YnQZfBm0GJzKLaKX63g5inoYiQKzCm5bkJ+hlolFyJUaGdGpEAH0BPtCxGEArjZ5OfjOiJVQLajbV9EdKJ+rcjg9CYchsZQjYN4u5sfhfrpVi98rPZJSkKCI+XdRNFcWYjm2hgdSCoxpaAK6lvZXyPmjgaM2b2IwBD3UgZ0xvrOtFLNlA4EFa5W3aMwy1M/K3n54u68VLmemZYnR+SYnBKPXJIKuSVUiOcPJIn8kJenWfnzflwPqelOWfWc0jmwvn6ARTAqZg=</latexit> Motivation transducers automata that transform combinatorial objects (’60s) abbaa . . . baaabab . . . . . . . .. bab . . . bbab . . . aabb . . . . . . . . . . . . . . .

  3. <latexit sha1_base64="Qs7Vli4OFN5bTSdrEC+NEFr6Js=">AB6nicbVDLSgNBEOyNrxhfUY9eBoPgKeyGiB6DXjxGzAuSJcxOepMhs7PLzKwQj7BiwdFvPpF3vwbJ8keNLGgoajqprsrSATXxnW/ndzG5tb2Tn63sLd/cHhUPD5p6ThVDJsFrHqBFSj4BKbhuBnUQhjQKB7WB8N/fbT6g0j2XDTBL0IzqUPOSMGis9NvqVfrHklt0FyDrxMlKCDPV+8as3iFkaoTRMUK27npsYf0qV4UzgrNBLNSaUjekQu5ZKGqH2p4tTZ+TCKgMSxsqWNGSh/p6Y0kjrSRTYzoiakV715uJ/Xjc14Y0/5TJDUq2XBSmgpiYzP8mA6QGTGxhDLF7a2EjaizNh0CjYEb/XldKqlL1q+eqhWqrdZnHk4QzO4RI8uIYa3EMdmsBgCM/wCm+OcF6cd+dj2ZpzsplT+APn8wfY5Y2F</latexit> <latexit sha1_base64="goaEZfstFv1SxfyiQGmTzJCr1Q=">ACL3icbZC7SgNBFIZn4y3GW9TSZjAIVmFXFC2DNpYRzAWSJZyZnSRDZi/MnBXCktansbHQVxEbsfUNLJ1cQJN4YODjP9f5WaKkQd9d3Irq2vrG/nNwtb2zu5ecf+gbuJUc1HjsYp1k4ERSkaihKVaCZaQMiUaLDBzTjfeBDayDi6x2Ei/B6kexKDmilTpEyYG0VxGgo+0UAxuiUO8WSW3YnQZfBm0GJzKLaKX63g5inoYiQKzCm5bkJ+hlolFyJUaGdGpEAH0BPtCxGEArjZ5OfjOiJVQLajbV9EdKJ+rcjg9CYchsZQjYN4u5sfhfrpVi98rPZJSkKCI+XdRNFcWYjm2hgdSCoxpaAK6lvZXyPmjgaM2b2IwBD3UgZ0xvrOtFLNlA4EFa5W3aMwy1M/K3n54u68VLmemZYnR+SYnBKPXJIKuSVUiOcPJIn8kJenWfnzflwPqelOWfWc0jmwvn6ARTAqZg=</latexit> <latexit sha1_base64="5vep7nCbjRhZ5rEQN9s1cI/sZFE=">ACGHicbVC7SgNBFJ2NrxhfUubwSBYhV1RtAzaWEYwD9iEcHd2Nhkyu7PM3BVCyGfYWOiv2ImtnX9i6STZwiQeGDic+zpzglQKg67RTW1jc2t4rbpZ3dvf2D8uFR06hM95gSirdDsBwKRLeQIGSt1PNIQ4kbwXDu2m9cS1ESp5xFHKuzH0ExEJBmglH4IAoCNDhaZXrhVdwa6SrycVEiOeq/80wkVy2KeIJNgjO+5KXbHoFEwySelTmZ4CmwIfe5bmkDMTXc8szyhZ1YJaS0fQnSmfp3YgyxMaM4sJ0x4MAs16bifzU/w+imOxZJmiFP2PxQlEmKik7/T0OhOUM5sgSYFtYrZQPQwNCmtHDFYAx6pEO7Y+qzI2Vg24YcSzYqbzmYVdK8qHqX1auHy0rtNg+tSE7IKTknHrkmNXJP6qRBGFHkmbySN+fFeXc+nM95a8HJZ47JApyvXxioOY=</latexit> <latexit sha1_base64="nOhyOz1a9+n1yoTrOBntVLqdNzQ=">AB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0WPRi8eK/YI2lM120y7dbMLuRCihP8GLB0W8+ou8+W/ctjlo64OBx3szMwLEikMu63U1hb39jcKm6Xdnb39g/Kh0ctE6ea8SaLZaw7ATVcCsWbKFDyTqI5jQLJ28H4bua3n7g2IlYNnCTcj+hQiVAwilZ6bPS9frniVt05yCrxclKBHPV+as3iFkacYVMUmO6npugn1GNgk+LfVSwxPKxnTIu5YqGnHjZ/NTp+TMKgMSxtqWQjJXf09kNDJmEgW2M6I4MsveTPzP6Y3viZUEmKXLHFojCVBGMy+5sMhOYM5cQSyrSwtxI2opoytOmUbAje8surpHVR9S6rVw+XldptHkcRTuAUzsGDa6jBPdShCQyG8Ayv8OZI58V5dz4WrQUnzmGP3A+fwDXY2E</latexit> <latexit sha1_base64="uWCbEYn82afSBWJvipScetRC9VA=">ACGnicbVC7SgNBFJ2NrxhfUubxSBYhV2JaBm0sYxgHpAs4c7sJBky+3DmrCEfIeNhf6Kndja+CeWziZbmMQDA4dz7p17ODSWQqPjfFuFtfWNza3idmlnd2/oHx41NJRohvskhGqkNBcylC3kSBkndixSGgkrfp+Dbz209caRGFD5jG3AtgGIqBYIBG8igAUKA96Ueo+WKU3VmsFeJm5MKydHol396fsSgIfIJGjdZ0YvQkoFEzyamXaB4DG8OQdw0NIeDam8xCT+0zo/j2IFLmhWjP1L8bEwi0TgNqJgPAkV72MvE/r5vg4NqbiDBOkIdsfmiQSBsjO2vA9oXiDGVqCDAlTFabjUABQ9PTwhWNAahU+eaPLGdPSmrGxhxLpip3uZhV0rqourXq5X2tUr/JSyuSE3JKzolLrkid3JEGaRJGHskzeSVv1ov1bn1Yn/PRgpXvHJMFWF+/sC2hvQ=</latexit> <latexit sha1_base64="RmSGkFbnLuSrGUxU6gAjYXqFA=">ACRXicbVDLSgMxFM34rPU16tJNsAiuykypj41QdOyQl/QliGTSdvQzIPkjlCG/olf48aF/oAf4U7EnWbaEfvwQuDc+4rx40EV2BZb8bK6tr6xmZuK7+9s7u3bx4cNlQYS8rqNBShbLlEMcEDVgcOgrUiyYjvCtZ0h7ep3nxgUvEwqMEoYl2f9APe45SAphzoiOEKwkdMsA1x8YdKX/TazynlWa0vGMWrKI1CbwM7AwUBZVx/zqeCGNfRYAFUSptm1F0E2IBE4FG+c7sWKRnk36rK1hQHymusnkf2N8qhkP90KpXwB4ws52JMRXauS7utInMFCLWkr+p7Vj6F1Ex5EMbCAThf1YoEhxKlZ2OSURAjDQiVXN+K6YBoD0BbOrdFgU/kSHp6Rnrn3OpVfaiMcugUSra5eL5fblQuclMy6FjdILOkI0uUQXdoSqI4oe0RN6Qa/Gs/FufBif09IVI+s5QnNhfP8AViGxhA=</latexit> Motivation transducers automata that transform combinatorial objects (’60s) abbaa . . . baaabab . . . . . . . .. bab . . . bbab . . . aabb . . . . . . . . . . . . . . . equivalence given J T 1 K = J T 2 K T 1 , , decide if T 2

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