Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-8448b6f56d-42gr6 Total loading time: 0 Render date: 2024-04-19T15:27:13.475Z Has data issue: false hasContentIssue false

Convergence Laws for Random Graphs

Published online by Cambridge University Press:  24 March 2017

By
J. F. Lynch
Edited by
Johann A. Makowsky  and
Elena V. Ravve
J. F. Lynch
Affiliation:
Department of Mathematics and Computer Science Clarkson University
Johann A. Makowsky
Affiliation:
Technion - Israel Institute of Technology, Haifa
Elena V. Ravve
Affiliation:
Technion - Israel Institute of Technology, Haifa
Get access

Summary

A summary is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.
Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Logic Colloquium '95 , pp. 115 - 133
Publisher: Cambridge University Press
Print publication year: 2017

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abiteboul, S. and Vianu, V. Generic computation and its complexity, in: Proc. 23rd ACM Symp. on Theory of Computing, Association for Computing Machinery, New York, 1991, 209–219.
Abiteboul, S., Compton, K. J. and Vianu, V. Queries are easier than you thought, probably, in: Proc. 11th ACM Symp. on Principles of Database Systems, Association for Computing Machinery, New York, 1992, 32–42.
Barwise, J., On Moschovakis closure ordinals, J. Symbolic Logic 42 (1977), 292–296.Google Scholar
Blass, A., Gurevich, Y. and Kozen, D. A zero-one law for logic with a fixed point operator, Inform, and Control 67 (1985), 70–90.Google Scholar
Bollobás, B. Random Graphs, Academic Press, London, 1985.
Compton, K. J. Henson, C. W. and Shelah, S. Nonconvergence, undecidability, and intractability in asymptotic problems, Ann. Pure Appl. Logic 36 (1987), 207–224.Google Scholar
Dolan, P. and Lynch, J. F. The logic of ordered random structures, Random Structures and Algorithms 4 (1993), 429–445.Google Scholar
Ehrenfeucht, A., An application of games to the completeness problem for formalized theories, Fund. Math. 49 (1961), 129–141.Google Scholar
Erdős, P. and Rényi, A. On random graphs, I, Pub. Math. (Debrecen) 6 (1959), 290–297.Google Scholar
Erdős, P. and Rényi, A. On the evolution of random graphs, Magyar Tud. Akad. Mat. Kutato Int. Kozl. 5 (1960), 17–61.Google Scholar
Fagin, R., Probabilities on finite models, J. Symbolic Logic 41 (1976), 50–58.Google Scholar
Fraïssé, R. Sur quelques classifications des systems de relations, Pub. Sci. Univ. Alger Sér. A 1 (1954), 35–182.Google Scholar
Glebskň, Y. V. Kogan, D. I. Liogon'kň, M. I. and Talanov, V. A. Range and degree of realizability of formulas in the restricted predicate calculus, Kibernetika (Kiev) 2 (1969), 17-28; English translation, Cybernetics 5 (1972), 142–154.Google Scholar
Kolaitis, Ph. G. On asymptotic probabilities of inductive queries and their decision problem, in Parikh, R. ed., Logics of Programs –85, Lecture Notes in Computer Science 193(1985), Springer-Verlag, 153–166.
Kolaitis, Ph. G. and Vardi, M. Y. Infmitary logics and 0-1 laws, Inform, and Computation 98 (1992), 258–294.Google Scholar
Lynch, J. F. Almost sure theories, Ann. Math. Logic 18 (1980), 91–135.Google Scholar
Lynch, J. F. Probabilities of first-order sentences about unary functions, Trans. A MS 287 (1985), 543–568.Google Scholar
Lynch, J. F. Probabilities of sentences about very sparse random graphs, Random Structures and Algorithms 3 (1992), 33–53.Google Scholar
Lynch, J. F. Infinitary logics and very sparse random graphs, in: Proc. 8th IEEE Symp. on Logic in Computer Science, IEEE Computer Society Press, Los Alamitos, 1993, 191-198. Also to appear in J. Symbolic Logic.
Lynch, J. F. An extension of 0-1 laws, Random Structures and Algorithms 5 (1994), 155–172.Google Scholar
Lynch, J. F. and Tyszkiewicz, J. The infinitary logic of sparse random graphs, in: Proc. 10th IEEE Symp. on Logic in Computer Science, IEEE Computer Society Press, Los Alamitos, 1995, 54–64.
Moschovakis, Y. N. Elementary Induction on Abstract Structures, North-Holland, 1974.
Mycielski, J., Measure and category of some sets of models, Notices AMS 22 (1975), A-475.Google Scholar
Palmer, E. M. Graphical Evolution, Wiley, New York, 1985.
Rosen, E., Shelah, S. Weinstein, S. k-Universal finite graphs, to appear in: Boppana, R. and Lynch, J. F. eds., Logic and Random Structures, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, American Mathematical Society, Providence.
Shelah, S., Very weak zero one laws for random graphs with order and random binary functions, Random Structures and Algorithms (to appear).
Shelah, S. and Spencer, J. Zero-one laws for sparse random graphs, J. AMS 1 (1988), 97–115.Google Scholar
Tyszkiewicz, J., Infinitary queries and their asymptotic probabilities. I. Properties definable in transitive closure logic, in: Borger, E. et al., eds., Proc. Computer Science Logic –91, Lecture Notes in Computer Science 626 (1991), Springer-Verlag, 396–410.

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×