On the Relative Complexity of Some Languages in NC

WE CONSIDER THE RELATIVE COMPLEXITY OF A NUMBER OF LANGUAGES KNOWN TO BE IN UNIFORM `NC(SUPERSCRIPT)1'', USING THE DESCRIPTIVE FRAMEWORK OF BARRINGTON, IMMERMAN, AND STRAUBING [4]. IN PARTICULAR WE SHARPEN SEVERAL RESULTS OF IBARRA, JIANG, AND RAVIKUMAR [9]. WE SHOW THAT THE ONE-SIDED DYCK LANGUAGES, STRUCTURED CFL''S, AND BRACKETED CFL''S ARE RECOGNIZABLE BY VERY UNIFORM FAMILIES OF THRESHOLD CIRCUITS (ARE IN DLOCTIME-UNIFORM TC(SUPERSCRIPT)0). WE SHOW THAT A LARGE CLASS OF DETERMINISTIC LINEAR CFL''S ARE IN UNIFORM TC(SUPERCRIPT)0, BUT THAT SOME ARE COMPLETE FOR UNIFORM NC(SUPERSCRIPT)1 (AND THUS NOT IN UNIFORM TC(SUPERSCRIPT)0 UNLESS TC(SUPERSCRIPT)0 = NC(SUPERSCRIPT)1 IN THE UNIFORM SETTING).

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