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The Isomorphism Problem for omega-Automatic Trees
[article]

2010
*
arXiv
*
pre-print

On

arXiv:1004.0610v1
fatcat:vxixr3av7fgl5fhxb23qvsgjtq
*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 ...##
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Tree-Automatic Well-Founded Trees

2013
*
Logical Methods in Computer Science
*

As an application of our result, we show that

doi:10.2168/lmcs-9(2:10)2013
fatcat:q5qbkycnzrdvrl6mlexjfcif4u
*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. ...##
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Model Theoretic Complexity of Automatic Structures
[article]

2008
*
arXiv
*
pre-print

We prove

arXiv:0809.3425v1
fatcat:fe4ravafabhetmaee2a5bh76li
*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. ...##
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Automatic Ordinals
[article]

2012
*
arXiv
*
pre-print

We prove that

arXiv:1205.1775v1
fatcat:pak5hs63ubctpfbtj2i56douy4
*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. ...##
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Generalized Symbolic Execution for Model Checking and Testing
[chapter]

2003
*
Lecture Notes in Computer Science
*

Our implementation

doi:10.1007/3-540-36577-x_40
fatcat:ux2t3ej35je43lt7xo7y6laefa
*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. ...##
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Symstra: A Framework for Generating Object-Oriented Unit Tests Using Symbolic Execution
[chapter]

2005
*
Lecture Notes in Computer Science
*

Tools such as Korat [8] are able to generate non-

doi:10.1007/978-3-540-31980-1_24
fatcat:tn3be5rapzbcrdzi7iyuirvo2a
*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. ...##
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Language Based Verification Tools for Functional Programs (Dagstuhl Seminar 16131)

2016
*
Dagstuhl Reports
*

While

doi:10.4230/dagrep.6.3.59
dblp:journals/dagstuhl-reports/GaboardiJJW16
fatcat:zeqdceqvzrgplfdpsbt6deoi2i
*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. ...##
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Cardinality and counting quantifiers on omega-automatic structures

2008
*
Symposium on Theoretical Aspects of Computer Science
*

We investigate structures that can be represented by

doi:10.4230/lipics.stacs.2008.1360
dblp:conf/stacs/KaiserRB08
fatcat:agsicc6vevdtphqnds67suinj4
*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. ...##
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Cardinality and counting quantifiers on omega-automatic structures
[article]

2008
*
arXiv
*
pre-print

We investigate structures that can be represented by

arXiv:0802.2866v1
fatcat:e6u444zcmzhepp56valkfilvqm
*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. ...##
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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. ...##
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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‘. ...##
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Mechanically verifying the correctness of the Fast Fourier Transform in ACL2
[chapter]

1998
*
Lecture Notes in Computer Science
*

Such simplicity in presentation facilitates reasoning about

doi:10.1007/3-540-64359-1_743
fatcat:37q5wu7n7rfodmtuzqjjsauyte
*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*. ...##
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Boosting Isomorphic Model Filtering with Invariants
[article]

2022
*
arXiv
*
pre-print

This paper proposes a novel approach to split

arXiv:2201.10516v1
fatcat:ucecule5szamvmmmlf6n4w7gsq
*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. ...##
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Finite and Algorithmic Model Theory (Dagstuhl Seminar 17361)

2018
*
Dagstuhl Reports
*

This report documents

doi:10.4230/dagrep.7.9.1
dblp:journals/dagstuhl-reports/DawarGKS17
fatcat:teyilwvdgrd6tch2gdb4d4dd5m
*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 ...##
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EXACT APPROXIMATIONS OF OMEGA NUMBERS

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

doi:10.1142/s0218127407018130
fatcat:cg66jt5o4vb4vni4hy34esld2y
*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. ...
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