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H.3.2 Tight satisfaction without local variables</div>
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Tight satisfaction is denoted by . For unclocked sequences without local variables, tight satisfaction is </p>
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defined as follows. w, x, y, z denote finite words over Σ. </p>
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? w b iff |w| = 1 and w0 b . </p>
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? w ( R ) iff w R . </p>
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? w ( R1 ##1 R2 ) iff there exist x, y such that w = xy and x R1 and y R2 . </p>
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? w ( R1 ##0 R2 ) iff there exist x, y, z such that w = xyz and |y| = 1, and xy R1 and yz R2 . </p>
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? w ( R1 or R2 ) iff either w R1 or w R2 . </p>
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? w ( R1 intersect R2 ) iff both w R1 and w R2 . </p>
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? w first_match ( R ) iff both </p>
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— w R and </p>
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— if there exist x, y such that w = xy and x R, then y is empty. </p>
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? w R [*0] iff |w| = 0. </p>
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? w R [*1:$] iff there exist words w1, w2,..., wj ( j > 1) such that w = w1w2...wj and for every i such that </p>
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1 < i < j, wi R . </p>
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If S is a clocked sequence, then w S iff w S’, where S’ is the unclocked sequence that results from S by </p>
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applying the rewrite rules. </p>
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An unclocked sequence R is non-degenerate iff there exists a non-empty finite word w over Σ such that </p>
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w R. A clocked sequence S is non-degenerate iff the unclocked sequence S’ that results from S by applying </p>
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the rewrite rules is non-degenerate.</p></div>
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