Formal languages
Syntactic Analysis and Operator Precedence
Journal of the ACM (JACM)
Journal of the ACM (JACM)
Balanced grammars and their languages
Formal and natural computing
Some properties of precedence languages
STOC '69 Proceedings of the first annual ACM symposium on Theory of computing
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Counter-Free Automata (M.I.T. research monograph no. 65)
Counter-Free Automata (M.I.T. research monograph no. 65)
Adding nesting structure to words
Journal of the ACM (JACM)
Journal of Computer and System Sciences
Parsing Techniques: A Practical Guide
Parsing Techniques: A Practical Guide
Synchronization of pushdown automata
DLT'06 Proceedings of the 10th international conference on Developments in Language Theory
Height-deterministic pushdown automata
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
Precedence automata and languages
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
State complexity of operations on input-driven pushdown automata
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
Operator precedence and the visibly pushdown property
Journal of Computer and System Sciences
TCS'12 Proceedings of the 7th IFIP TC 1/WG 202 international conference on Theoretical Computer Science
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Operator precedence languages, designated as Floyd's Languages (FL) to honor their inventor, are a classical deterministic context-free family. FLs are known to be a boolean family, and have been recently shown to strictly include the Visibly Pushdown Languages (VPDL); the latter are FLs characterized by operator precedence relations determined by the alphabet partition. In this paper we give the non-obvious proves that FLs have the same closure properties that motivated the introduction of VPDLs, namely under reversal, concatenation and Kleene's star. Thus, rather surprisingly, the historical FL family turns out to be the largest known deterministic context-free family that includes the VPDL and has the same closure properties needed for applications to model checking and for defining mark-up languages such as HTML. As a corollary, an extended regular expression of precedence-compatible FLs is a FL and a deterministic parser for it can be algorithmically obtained.