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| Stephan Kreutzer, "Expressive Equivalence of Least and Inflationary Fixed-Point Logic," Logic in Computer Science, Symposium on, pp. 403, 17th Annual IEEE Symposium on Logic in Computer Science (LICS'02), 2002. | |||
| BibTex | x | ||
| @article{ 10.1109/LICS.2002.1029848, author = {Stephan Kreutzer}, title = {Expressive Equivalence of Least and Inflationary Fixed-Point Logic}, journal ={Logic in Computer Science, Symposium on}, volume = {0}, year = {2002}, issn = {1043-6871}, pages = {403}, doi = {http://doi.ieeecomputersociety.org/10.1109/LICS.2002.1029848}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, } | |||
| RefWorks Procite/RefMan/Endnote | x | ||
| TY - CONF JO - Logic in Computer Science, Symposium on TI - Expressive Equivalence of Least and Inflationary Fixed-Point Logic SN - 1043-6871 SP EP A1 - Stephan Kreutzer, PY - 2002 KW - null VL - 0 JA - Logic in Computer Science, Symposium on ER - | |||
We study the relationship between least and inflationary fixed-point logic. By results of Gurevich and Shelah from 1986, it has been known that on finite structures both logics have the same expressive power. On infinite structures however, the question whether there is a formula in IFP not equivalent to any LFP-formula was still open.
In this paper, we settle the question by showing that both logics are equally expressive on arbitrary structures. The proof will also establish the strictness of the nesting-depth hierarchy for IFP on some infinite structures. Finally, we show that the alternation hierarchy for IFP collapses to the first level on all structures, i.e. the complement of an inflationary fixed-point is an inflationary fixed-point itself.