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Recursive descent parsing for Boolean grammars

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Abstract

The recursive descent parsing method for the context-free grammars is extended for their generalization, Boolean grammars, which include explicit set-theoretic operations in the formalism of rules and which are formally defined by language equations. The algorithm is applicable to a subset of Boolean grammars. The complexity of a direct implementation varies between linear and exponential, while memoization keeps it down to linear.

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References

  1. Aho A.V., Sethi R. and Ullman J.D. (1986). Compilers: principles, techniques and tools. Addison-Wesley, Reading

    Google Scholar 

  2. Birman A. and Ullman J.D. (1973). Parsing algorithms with backtrack. Inf. Control 23: 1–134

    Article  MathSciNet  Google Scholar 

  3. Ford, B.: Parsing expression grammars: a recognition-based syntactic foundation. Proceedings of POPL 2004 (Venice, Italy, January 14–16, 111–122 2004)

  4. Ginsburg S. and Rice H.G. (1962). Two families of languages related to ALGOL. J. ACM 9: 350–371

    Article  MathSciNet  Google Scholar 

  5. Greibach S.A. (1965). A new normal-form theorem for context-free phrase structure grammars. J. ACM 12: 42–52

    Article  MATH  MathSciNet  Google Scholar 

  6. Grune D. and Jacobs C.J.H. (1988). A programmer-friendly LL(1) parser generator. Softw. Pract. Exp. 18(1): 29–38

    Article  Google Scholar 

  7. Ichbiah J., Barnes J.G.P., Firth R.J. and Woodger M. (1991). Rationale for the design of the Ada programming language. Cambridge University Press, Cambridge

    Google Scholar 

  8. Knuth D.E. (1971). Top-down syntax analysis. Acta Informatica 1: 79–110

    Article  MATH  Google Scholar 

  9. Kountouriotis, V., Nomikos, Ch., Rondogiannis, P.: Well-founded semantics for Boolean grammars. Developments in Language Theory (DLT 2006, Santa Barbara, USA, June 26–29, 2006), LNCS 4036, 203–214

  10. Kurki-Suonio R. (1969). Notes on top-down languages. BIT 9: 225–238

    Article  MATH  Google Scholar 

  11. Lewis P.M. and Stearns R.E. (1968). Syntax-directed transduction. J. ACM 15(3): 465–488

    Article  MATH  Google Scholar 

  12. Megacz A. (2006). Scannerless Boolean parsing. Electron. Notes Theor. Comput. Sci. 164(2): 97–102

    Article  Google Scholar 

  13. Norvig P. (1991). Techniques for automatic memoization with applications to context-free parsing. Comput. Linguistics 17(1): 91–98

    Google Scholar 

  14. Okhotin A. (2001). Conjunctive grammars. J. Automata Lang. Combinatorics 6(4): 519–535

    MATH  MathSciNet  Google Scholar 

  15. Okhotin A. (2002). Top-down parsing of conjunctive languages. Grammars 5(1): 21–40

    Article  MATH  MathSciNet  Google Scholar 

  16. Okhotin A. (2004). Boolean grammars. Inf. Comput. 194(1): 19–48

    Article  MATH  MathSciNet  Google Scholar 

  17. Okhotin A. (2005). The dual of concatenation. Theor. Comput. Sci. 345(2–3): 425–447

    Article  MATH  MathSciNet  Google Scholar 

  18. Okhotin A. (2006). Generalized LR parsing algorithm for Boolean grammars. Int. J. Found. Comput. Sci. 17(3): 629–664

    Article  MATH  MathSciNet  Google Scholar 

  19. Parr T.J. and Quong R.W. (1995). ANTLR: a predicated-LL(k) parser generator. Softw. Pract. Exp. 25(7): 789–810

    Article  Google Scholar 

  20. Rozenkrantz D.J. and Stearns R.E. (1970). Properties of deterministic top-down grammars. Inf. Control 17: 226–256

    Article  Google Scholar 

  21. Wood D. (1969). The theory of left factored languages. (I, II). Comput. J. 12(4, 349–356): 12–4, 349356

    Google Scholar 

  22. Wood D. (1970). The theory of left factored languages. (I, II). Comput. J. 13(1): 55–62

    Article  MATH  MathSciNet  Google Scholar 

  23. Wrona, M.: Stratified Boolean grammars mathematical foundations of computer science. In: Proceedings of MFCS 2005, Gdansk, Poland, August 29–September 2, 2005. LNCS, vol. 3618, pp. 801–812 (2005)

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Authors and Affiliations

  1. Department of Mathematics, University of Turku, Turku, 20014, Finland

    Alexander Okhotin

  2. Academy of Finland, Vilhonvuorenkatu 6, Helsinki, 00501, Finland

    Alexander Okhotin

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  1. Alexander Okhotin
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Correspondence to Alexander Okhotin.

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Supported by the Academy of Finland under grant 118540.

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Okhotin, A. Recursive descent parsing for Boolean grammars. Acta Informatica 44, 167–189 (2007). https://doi.org/10.1007/s00236-007-0045-0

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  • DOI: https://doi.org/10.1007/s00236-007-0045-0

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