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The Isomorphism Problem for omega-Automatic Trees [article]

Dietrich Kuske, Jiamou Liu, Markus Lohrey
2010 arXiv   pre-print
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

Martin Huschenbett, Alexander Kartzow, Jiamou Liu, Markus Lohrey, Anuj Dawar
2013 Logical Methods in Computer Science  
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]

Bakhadyr Khoussainov, Mia Minnes
2008 arXiv   pre-print
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]

Olivier Finkel
2012 arXiv   pre-print
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]

Sarfraz Khurshid, Corina S. PĂsĂreanu, Willem Visser
2003 Lecture Notes in Computer Science  
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]

Tao Xie, Darko Marinov, Wolfram Schulte, David Notkin
2005 Lecture Notes in Computer Science  
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)

Marco Gaboardi, Suresh Jagannathan, Ranjit Jhala, Stephanie Weirich, Marc Herbstritt
2016 Dagstuhl Reports  
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

Lukasz Kaiser, Sasha Rubin, Vince Bárány, Marc Herbstritt
2008 Symposium on Theoretical Aspects of Computer Science  
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]

Lukasz Kaiser, Sasha Rubin, Vince Bárány
2008 arXiv   pre-print
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  
(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  
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]

Ruben A. Gamboa
1998 Lecture Notes in Computer Science  
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]

João Araújo, Choiwah Chow, Mikoláš Janota
2022 arXiv   pre-print
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)

Anuj Dawar, Erich Grädel, Phokion G. Kolaitis, Thomas Schwentick, Marc Herbstritt
2018 Dagstuhl Reports  
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

CRISTIAN S. CALUDE, MICHAEL J. DINNEEN
2007 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering  
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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