## Automaton transformations and regular definability |

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2n+l)-track A*XB accept the tape accepts a tape accepts the set agrees letter-for-letter automata and regular automaton transformation automaton tTL automaton which reads auxiliary letter auxiliary symbol checks for membership Clement Leo McGowan concatenation construct an automaton convenience CORNELL UNIVERSITY LIBRARY Corollary 4.1 define an automaton Define the sentence definition empty set empty tape encoding equal length event is regular finite alphabet finite automaton ZTL finite Cartesian product finite sets function Given a finite Hence initial segment input j-th track left-mark Lemma letter-for-letter with Track-(2n+2 m-i+l)-times maps an event non-empty one-many map preserve regularity Proof reads n-track tapes reads two-track tapes REGULAR DEFINABILITY regular event regular injection relation represented School of Cornell second track semigroup set of tapes substitutions which preserve subword supplement Sg tape seg tape segment tape square Theorem Track-(2n+l Track-i TRANSFORMATIONS AND REGULAR u-erasing projection ular event