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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  ...  This also complements a very recent result of Hjörth, Khoussainov, Montalban and Nies showing that there is an omega-automatic structure which has no injective presentation.  ...  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  ...  This also complements a very recent result of Hjörth, Khoussainov, Montalban and Nies showing that there is an omega-automatic structure which has no injective presentation.  ...  Acknowledgment We thank the referees for detailed technical remarks and corrections.  ... 
arXiv:0802.2866v1 fatcat:e6u444zcmzhepp56valkfilvqm

On Decidability Properties of One-Dimensional Cellular Automata [article]

Olivier Finkel
2009 arXiv   pre-print
Then, applying recent results of Kuske and Lohrey on omega-automatic structures, it follows that the first-order theory, extended with some counting and cardinality quantifiers, of the structure S_A, is  ...  We first show that, for each one-dimensional cellular automaton A, the phase-space S_A is an omega-automatic structure.  ...  We hope that the interplay of the two domains of cellular automata and of automatic structures will be fruitful and will provide new results in both fields of research.  ... 
arXiv:0903.4615v2 fatcat:fc5ccknkefdildt3lk7whl5xfi

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".  ...  We formalize agent-based models as stochastic processes whose states are metafinite models, and we define a notion of abstraction.  ...  Our main results are conditions that imply an abstraction is sound, and further conditions that imply it preserves the Markov property.  ... 
doi:10.4230/dagrep.7.9.1 dblp:journals/dagstuhl-reports/DawarGKS17 fatcat:teyilwvdgrd6tch2gdb4d4dd5m

Page 3624 of Mathematical Reviews Vol. , Issue 89G [page]

1989 Mathematical Reviews  
Polymorphic lambda calculus has four sorts of objects, called orders, operators, types and terms. The types make up an order called Omega.  ...  One may regard G as a contravari- ant functor from S to the category of small categories, functors and natural transformations, effectively giving a categorical structure externally to the object Omega  ... 

Function composition and automatic average case analysis

Paul Zimmermann
1995 Discrete Mathematics  
We define the composition of functions defined over extended context-free languages. We show that this composition is automatically computable.  ...  It enables the automatic analysis of complex problems with small input descriptions, for example repeated differentiation or iterated automata on regular languages.  ...  all data structures are lists, or explicitly like in Lambda-Upsilon-Omega.  ... 
doi:10.1016/0012-365x(94)00146-a fatcat:ear4qr6blrffxbbokmitb5c67m

Statistical study of auroral omega bands

Noora Partamies, James M. Weygand, Liisa Juusola
2017 Annales Geophysicae  
</strong> The presence of very few statistical studies on auroral omega bands motivated us to test-use a semi-automatic method for identifying large-scale undulations of the diffuse aurora boundary and  ...  These findings support the theory that omegas are produced by fast earthward flows and auroral streamers, despite the rarity of good conjugate observations.</p>  ...  The authors thank Sanna Mäkinen, Jyrki Mattanen, Anneli Ketola, Tero Raita and Carl-Fredrik Enell for careful maintenance of the camera network and data flow, and Mikko Syrjäsuo for implementing the random  ... 
doi:10.5194/angeo-35-1069-2017 fatcat:bthv3qcwnvh63hjrtjmas2ewf4

Interlingual Annotation for MT Development [chapter]

Florence Reeder, Bonnie Dorr, David Farwell, Nizar Habash, Stephen Helmreich, Eduard Hovy, Lori Levin, Teruko Mitamura, Keith Miller, Owen Rambow, Advaith Siddharthan
2004 Lecture Notes in Computer Science  
In this paper, we describe the creation of an interlingua and the development of a corpus of semantically annotated text, to be validated in six languages and evaluated in several ways.  ...  We present the annotation tools built and outline the annotation process. Following this, we describe our evaluation methodology and conclude with a summary of issues that have arisen.  ...  Half of the sites marked one translation first, and the other half of the sites marked the second translation first.  ... 
doi:10.1007/978-3-540-30194-3_26 fatcat:67rre7wl4fernonqeu2x44nhgu

Automatic average-case analysis of algorithms

Philippe Flajolet, Bruno Salvy, Paul Zimmermann
1991 Theoretical Computer Science  
A fair fragment of this theory is also incorporated into a system called Lambda-Upsilon-Omega.  ...  We then present some major components of the associated asymptotic theory and exhibit a class of naturally arising functions that can be automatically analyzed.  ...  Expression(z) = C Expression,, l z" and rdiff(z) = C rdiff,, l z". n=O na0 The first one is the standard counting generating function of the expression structures.  ... 
doi:10.1016/0304-3975(91)90145-r fatcat:yoecav3wjnhpnkc4z2tkoi42uu

Don't Forget the Model in Your Model-based Reliability Coefficients: A Reply to McNeish (2018)

Victoria Savalei, Steven P. Reise
2019 Collabra: Psychology  
First, we show that McNeish exaggerates the extent to which alpha is different from omega when unidimensionality holds.  ...  on an exploratory bifactor solution ("Revelle's omega total"), and the glb ("greatest lower bound").  ...  If the structure of the scale is best conceptualized as a correlated factors model or a second-order factor model, omega total will capture the variance due to all the extracted factors.  ... 
doi:10.1525/collabra.247 fatcat:laee7a7jfvguzdswuosqx3njt4

The Isomorphism Problem for omega-Automatic Trees [article]

Dietrich Kuske, Jiamou Liu, Markus Lohrey
2010 arXiv   pre-print
The main result of this paper is that the isomorphism for omega-automatic trees of finite height is at least has hard as second-order arithmetic and therefore not analytical.  ...  This strengthens a recent result by Hjorth, Khoussainov, Montalban, and Nies showing that the isomorphism problem for omega-automatic structures is not Σ^1_2.  ...  One of the main motivations for investigating automatic graphs is that their first-order theories can be decided uniformly (i.e., the input is an automatic presentation and a first-order sentence).  ... 
arXiv:1004.0610v1 fatcat:vxixr3av7fgl5fhxb23qvsgjtq

The mate-in-n problem of infinite chess is decidable [article]

Dan Brumleve and Joel David Hamkins and Philipp Schlicht
2012 arXiv   pre-print
The proof proceeds by showing that the mate-in-n problem is expressible in what we call the first-order structure of chess, which we prove (in the relevant fragment) is an automatic structure, whose theory  ...  Nevertheless, the main theorem of this article, confirming a conjecture of the first author and C. D. A.  ...  Since the structure Ch A is automatic, it follows by the decidability theorem of automatic structures [KN95, BG00] that the first-order theory of this structure is uniformly decidable.  ... 
arXiv:1201.5597v4 fatcat:3ujxrrkx4rgsbicrjwgquuo6my

The Mate-in-n Problem of Infinite Chess Is Decidable [chapter]

Dan Brumleve, Joel David Hamkins, Philipp Schlicht
2012 Lecture Notes in Computer Science  
The proof proceeds by showing that the mate-in-n problem is expressible in what we call the first-order structure of chess Ch, which we prove (in the relevant fragment) is an automatic structure, whose  ...  This issue is connected with transfinite game values in infinite chess, and the exact value of the omega one of chess ω chess 1 is not known.  ...  Since the structure Ch A is automatic, it follows by the decidability theorem of automatic structures [KN95, BG00] that the first-order theory of this structure is uniformly decidable.  ... 
doi:10.1007/978-3-642-30870-3_9 fatcat:6ob5b6nxcnd63gzftp3n57gqz4

Cystic Fibrosis%3A Computing the World's First Cure for a Genetic Disease

James Bonnar
2016 Figshare  
A new computational approach, called the omega algorithm, is developed, implemented and applied to find compounds that could potentially correct the delta F508 mutation responsible for cystic fibrosis.  ...  Cystic fibrosis (CF) affects millions of people worldwide.  ...  We can t a Markov model of order 0 to a specic piece of text by counting the number of occurrences of each letter in that text, and using these counts as probabilities.  ... 
doi:10.6084/m9.figshare.4104021.v1 fatcat:2j5fwnnzi5eiljegu3d4gremqi

Lambda-Upsilon-Omega: An assistant algorithms analyzer [chapter]

Philippe Flajolet, Bruno Salvy, Paul Zimmermann
1989 Lecture Notes in Computer Science  
Lambda-Upsilon-Omega, , is a system designed to perform automatic analysis of well-de ned classes of algorithms operating over \decomposable" data structures.  ...  The algebraic part relies on recent methodologies in combinatorial analysis based on systematic correspondences between structural type de nitions and counting generating functions.  ...  Lambda-Upsilon-Omega, , is a system designed to perform automatic analysis of well-de ned classes of algorithms operating over \decomposable" data structures.  ... 
doi:10.1007/3-540-51083-4_60 fatcat:5jvqldbvxzdi3k4h5347lvcp34
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