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The Isomorphism Problem for omega-Automatic Trees
[article]
2010
arXiv
pre-print
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On the way to our main results, we show lower and upper bounds for the isomorphism problem for omega-automatic trees of every finite height: (i) It is decidable (Π^0_1-complete, resp,) for height 1 (2, ...
Moreover, assuming the continuum hypothesis CH, we can show that the isomorphism problem for omega-automatic trees of finite height is recursively equivalent with second-order arithmetic. ...
But the isomorphism problem for ω-automatic trees of height 3 is hard for Π 1 1 (and therefore outside of the arithmetical hierarchy) while the isomorphism problem for automatic trees of height 3 is Π ...
arXiv:1004.0610v1
fatcat:vxixr3av7fgl5fhxb23qvsgjtq
Tree-Automatic Well-Founded Trees
2013
Logical Methods in Computer Science
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As an application of our result, we show that the isomorphism problem for tree-automatic well-founded trees is complete for level Delta^0_omega^omega of the hyperarithmetical hierarchy with respect to ...
Using Delhomme's decomposition technique for tree-automatic structures, we show that the (ordinal) rank of a tree-automatic well-founded tree is strictly below omega^omega. ...
In particular, we thank one of the referees for simplifying our arguments in Example 3.27. ...
doi:10.2168/lmcs-9(2:10)2013
fatcat:q5qbkycnzrdvrl6mlexjfcif4u
Model Theoretic Complexity of Automatic Structures
[article]
2008
arXiv
pre-print
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We prove the following results: 1) The ordinal height of any automatic well- founded partial order is bounded by \omega^\omega ; 2) The ordinal heights of automatic well-founded relations are unbounded ...
Moreover, there are automatic structures of Scott rank the first non-computable ordinal and its successor; 4) For any computable ordinal, there is an automatic successor tree of Cantor-Bendixson rank that ...
Again, this result can be used to show that the isomorphism problem for automatic Boolean algebras is decidable. ...
arXiv:0809.3425v1
fatcat:fe4ravafabhetmaee2a5bh76li
Automatic Ordinals
[article]
2012
arXiv
pre-print
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We prove that the injectively omega-tree-automatic ordinals are the ordinals smaller than ω^ω^ω. ...
Then we show that the injectively ω^n-automatic ordinals, where n>0 is an integer, are the ordinals smaller than ω^ω^n. ...
We thank the anonymous referees for useful comments on a preliminary version of this paper. ...
arXiv:1205.1775v1
fatcat:pak5hs63ubctpfbtj2i56douy4
Generalized Symbolic Execution for Model Checking and Testing
[chapter]
2003
Lecture Notes in Computer Science
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Our implementation for Java uses the Java PathFinder model checker. ...
The program instrumentation enables a model checker to automatically explore different program heap configurations and manipulate logical formulae on program data (using a decision procedure). ...
Acknowledgements The authors would like to thank Doron Peled for useful discussions and Viktor Kuncak, Darko Marinov, Zhendong Su, and the anonymous referees for useful comments. ...
doi:10.1007/3-540-36577-x_40
fatcat:ux2t3ej35je43lt7xo7y6laefa
Symstra: A Framework for Generating Object-Oriented Unit Tests Using Symbolic Execution
[chapter]
2005
Lecture Notes in Computer Science
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Tools such as Korat [8] are able to generate non-isomorphic object graphs that can be used for testing, but they do not generate covering test sequences. ...
Symbolic execution is the foundation of static code analysis tools. These tools typically do not generate test data, but automatically verify simple properties of programs. ...
We also thank Wolfgang Grieskamp, Sarfraz Khurshid, Viktor Kuncak, and Nikolai Tillmann for useful discussions on this work and anonymous reviewers for the comments on a previous version of this paper. ...
doi:10.1007/978-3-540-31980-1_24
fatcat:tn3be5rapzbcrdzi7iyuirvo2a
Language Based Verification Tools for Functional Programs (Dagstuhl Seminar 16131)
2016
Dagstuhl Reports
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While the research community has studied the problem of language based verification for imperative and first-order programs for decades -yielding important ideas like Floyd-Hoare Logics, Abstract Interpretation ...
This report documents the program and the outcomes of Dagstuhl Seminar 16131 "Language Based Verification Tools for Functional Programs". ...
for tree automata inclusion. ...
doi:10.4230/dagrep.6.3.59
dblp:journals/dagstuhl-reports/GaboardiJJW16
fatcat:zeqdceqvzrgplfdpsbt6deoi2i
Cardinality and counting quantifiers on omega-automatic structures
2008
Symposium on Theoretical Aspects of Computer Science
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We investigate structures that can be represented by omega-automata, so called omega-automatic structures, and prove that relations defined over such structures in first-order logic expanded by the first-order ...
The proof identifies certain algebraic properties of omega-semigroups. As a consequence an omega-regular equivalence relation of countable index has an omega-regular set of representatives. ...
Acknowledgment We thank the referees for detailed technical remarks and corrections. ...
doi:10.4230/lipics.stacs.2008.1360
dblp:conf/stacs/KaiserRB08
fatcat:agsicc6vevdtphqnds67suinj4
Cardinality and counting quantifiers on omega-automatic structures
[article]
2008
arXiv
pre-print
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We investigate structures that can be represented by omega-automata, so called omega-automatic structures, and prove that relations defined over such structures in first-order logic expanded by the first-order ...
The proof identifies certain algebraic properties of omega-semigroups. As a consequence an omega-regular equivalence relation of countable index has an omega-regular set of representatives. ...
Acknowledgment We thank the referees for detailed technical remarks and corrections. ...
arXiv:0802.2866v1
fatcat:e6u444zcmzhepp56valkfilvqm
Page 2219 of Mathematical Reviews Vol. , Issue 91D
[page]
1991
Mathematical Reviews
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(F-PARIS7-LI)
Pushdown automata on infinite trees and omega-Kleene closure of context-free tree sets. ...
We also obtain a self- correcting algorithm, optimal with respect to order, for a sorting problem of a set that is isomorphic to a Boolean algebra.”
91d:68010 68P15
Tenenbaum, L. A. ...
Page 3624 of Mathematical Reviews Vol. , Issue 89G
[page]
1989
Mathematical Reviews
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Inspired by the author’s categorical presentation, but seeking to avoid the semantic problem of equality “up to isomorphism” of category theory, T. Coquand and T. ...
“Contrary to the case of finite developments in our earlier paper [op. cit.], the method of exact estimates does not automatically result in a simpler strong normalization proof for A‘. ...
Mechanically verifying the correctness of the Fast Fourier Transform in ACL2
[chapter]
1998
Lecture Notes in Computer Science
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Such simplicity in presentation facilitates reasoning about the resulting algorithms, and in fact Misra was able to give a stunningly simple proof of the correctness of the FFT. ...
In [10] , Misra introduced the powerlist data structure, which is well suited to express recursive, data-parallel algorithms. ...
Often, we will be interested in p-similar-p powerlists, which are those with isomorphic tie trees. ...
doi:10.1007/3-540-64359-1_743
fatcat:37q5wu7n7rfodmtuzqjjsauyte
Boosting Isomorphic Model Filtering with Invariants
[article]
2022
arXiv
pre-print
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This paper proposes a novel approach to split the generated models into mutually non-isomorphic blocks. ...
However, it is hindered by the possible existence of many isomorphic models, which usually only add noise. ...
Acknowledgments The results were supported by the Ministry of Education, Youth and Sports within the dedicated program ERC CZ under the project POSTMAN no. ...
arXiv:2201.10516v1
fatcat:ucecule5szamvmmmlf6n4w7gsq
Finite and Algorithmic Model Theory (Dagstuhl Seminar 17361)
2018
Dagstuhl Reports
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This report documents the program and the outcomes of Dagstuhl Seminar 17361 "Finite and Algorithmic Model Theory". ...
Our main results are conditions that imply an abstraction is sound, and further conditions that imply it preserves the Markov property. ...
In particular, we prove that the class of all torsion-free Abelian groups of rank one is uniformly omega-automatic and that there are uniform omega-tree-automatic presentation of the class of all Abelian ...
doi:10.4230/dagrep.7.9.1
dblp:journals/dagstuhl-reports/DawarGKS17
fatcat:teyilwvdgrd6tch2gdb4d4dd5m
EXACT APPROXIMATIONS OF OMEGA NUMBERS
2007
International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
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Turing machine, which is universal when used with data in base 16 or base 2: we compute 43 exact bits for the base 16 machine and 40 exact bits for the base 2 machine. ...
The value of an Omega number is highly machine-dependent. ...
Acknowledgement We thank Ivy Jiang and Simona Mancaş who helped us write (and debug) preliminary versions of the Java simulator for the register machine language(s) described here. ...
doi:10.1142/s0218127407018130
fatcat:cg66jt5o4vb4vni4hy34esld2y
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