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Upper Bounds on Height of Terms in a Solution of a Semiunification Problem

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Abstract

In this paper, we investigate a decidable case of the term semiunification problem. In our case, the arity of any functional symbol in terms equals one (with a possible exception for outer symbols of terms, for which no restrictions are imposed). We propose an algorithm constructing the most general solution of the semiunification problem. In addition, we prove an upper bound on the height of this solution; this upper bound is linear with respect to heights of terms in the initial problem. Our method reduces the problem for terms to a special system of equations in free semigroups and solves the latter system. Bibliography: 10 titles.

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REFERENCES

  1. G. S. Makanin, “The problem of solvability of equations in a free semigroup,” Mat.Sb.,103, 147–236 (1997).

    Google Scholar 

  2. V. P. Orevkov, “Upper bounds on deduction lengthening after cut elimination,” Zap.Nauchn.Semin.LOMI, 176,132–146 (1988).

    Google Scholar 

  3. V. P. Orevkov, “Systems of equations in terms with substitutions,” in: Problems of Cybernetics,Moscow (1988), pp.127–148.

  4. B. Konev, “Upper bound on the height of terms in proofs with cuts,” in: Proceedings of First-Order Theorem Proving —FTP’ 98 /2nd International Workshop on First-Order Theorem Proving,Vienna (1998), pp.162–172.

  5. J. A. Robinson, “A machine oriented logic based on resolution principle,” J.Assoc.Comput.Mach.,12, 23–41 (1965).

    Google Scholar 

  6. V. P. Orevkov, Complexity of Proofs and Their Transformations in Axiomatic Theories, Am.Math.Soc. (1991).

  7. M. Baaz, “Note on the existence of most general semi-unifiers,” in: Arith.,Proof Theory and Comput.Com-plexity, Oxford University Press (1993), pp.20–29.

  8. M. Baaz and G. Salzer, “Semi-unification and generalizations of a particularly simple form,” Lect.Notes Comp.Sci., 135–148 (1995).

  9. A. J. Kfoury, J.Tiuryn, and P. Urzyczyn, “The undecidability of the semi-uni cation problem,” BUCS Tech. Report (1989).

  10. P. Pudlák, “On a unification problem related to Kreisel 's conjecture,” Comm.Math.Univ.Carolinae,23, 551–556 (1988).

    Google Scholar 

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  1. St.Petersburg Department of the, Steklov Mathematical Institute, Russia

    V. B. Zhizhkun

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  1. V. B. Zhizhkun
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Zhizhkun, V.B. Upper Bounds on Height of Terms in a Solution of a Semiunification Problem. Journal of Mathematical Sciences 118, 4966–4981 (2003). https://doi.org/10.1023/A:1025649322682

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  • DOI: https://doi.org/10.1023/A:1025649322682

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