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Modular Quantifiers [chapter]

Howard Straubing
1994 Finite Automata, Formal Logic, and Circuit Complexity  
The study of languages defined with modular quantifiers, the subject of the present survey, began with this collaboration. 1 Generalized First-order Formulas over < First-Order Logic and Star-free Sets  ...  He showed that the levels of the dot-depth hierarchy corresponded precisely to level of the quantifier alternation hierarchy within first-order logic [26] , and applied Ehrenfeucht-Fraïssé games to prove  ...  q (in the case of modular quantifiers).  ... 
doi:10.1007/978-1-4612-0289-9_7 fatcat:jn5teolrhrf3tfysd3dnrku7qu

Languages Defined with Modular Counting Quantifiers

Howard Straubing
2001 Information and Computation  
We prove that a regular language defined by a boolean combination of generalized 1 -sentences built using modular counting quantifiers can be defined by a boolean combination of 1 -sentences in which only  ...  (The universal quantifier is obtained from the existential quantifier by negation.) A formula without free variables is called a sentence.  ...  The new quantifiers are denoted ∃ (i,s, p) , where s ≥ 0, p > 0, and 0 ≤ i < s + p.  ... 
doi:10.1006/inco.2000.2923 fatcat:oc5wtxnb55gezezhx66qofl2oi

Quantifier Elimination for Linear Modular Constraints [chapter]

Ajith K. John, Supratik Chakraborty
2014 Lecture Notes in Computer Science  
We present an efficient and bit-precise algorithm for quantifier elimination from conjunctions of linear modular constraints.  ...  We have extended the above algorithm to work with boolean combinations of linear modular constraints as well.  ...  In contrast to bit-blasting and PA-based techniques, our techniques keep the quantifier-eliminated formula in linear modular arithmetic, so that it is amenable to further bit-vector level reasoning.  ... 
doi:10.1007/978-3-662-44199-2_46 fatcat:ru53a52krfexfffsst3z6va7qm

One Quantifier Alternation in First-Order Logic with Modular Predicates [article]

Manfred Kufleitner, Tobias Walter
2014 arXiv   pre-print
Adding modular predicates yields a generalization of first-order logic FO over words.  ...  The fragment Sigma2 consists of first-order formulas in prenex normal form with two blocks of quantifiers starting with an existential block.  ...  Acknowledgements We thank Luc Dartois, Alexander Lauser, and Charles Paperman for several fruitful discussions on modular predicates, we thank Volker Diekert for discussions on the proof of Lemma 5.6,  ... 
arXiv:1310.5043v3 fatcat:iodrsgpo4bhqvd736nc5twgxde

From Strong Amalgamability to Modularity of Quantifier-Free Interpolation [article]

Roberto Bruttomesso, Silvio Ghilardi, Silvio Ranise
2012 arXiv   pre-print
We show that a sufficient and necessary condition to do this for quantifier-free interpolation is that the component theories have the 'strong (sub-)amalgamation' property.  ...  Then, we provide an equivalent syntactic characterization, identify a sufficient condition, and design a combined quantifier-free interpolation algorithm capable of handling both convex and non-convex  ...  This paper studies the modularity of quantifier-free interpolation.  ... 
arXiv:1203.3730v2 fatcat:eqrsvr6qobebdmm3z54zpat62q

Quantifying Advantages of Modular Construction: Waste Generation

Loizos Loizou, Khalegh Barati, Xuesong Shen, Binghao Li
2021 Buildings  
This paper aims to quantify these differences.  ...  This reduces the research gap of quantifying the waste differences between conventional and modular construction, and provides thoroughly researched waste rates for future research, while also improving  ...  Table 1 . 1 Summary of previous literature on quantifying modular construction. Table 1 . 1 Cont.  ... 
doi:10.3390/buildings11120622 doaj:03269d8c144a49ed977fed1fa2bd0786 fatcat:xqxwuno645e6nfiqgpcgmfdcma

Quantifying Modularity in the Evolution of Biomolecular Systems

B. Snel
2004 Genome Research  
A third issue is how to quantify modularity.  ...  The main aim of this statistic is to quantify how nonrandom or modular the evolution of the functional modules in a data set is, in addition to the average modularity score.  ... 
doi:10.1101/gr.1969504 pmid:14993205 pmcid:PMC353226 fatcat:tmtvam5befcxraiwkmmlj6uawi

From Strong Amalgamability to Modularity of Quantifier-Free Interpolation [chapter]

Roberto Bruttomesso, Silvio Ghilardi, Silvio Ranise
2012 Lecture Notes in Computer Science  
We show that a sufficient and necessary condition to do this for quantifier-free interpolation is that the component theories have the 'strong (sub-)amalgamation' property.  ...  Then, we provide an equivalent syntactic characterization, identify a sufficient condition, and design a combined quantifier-free interpolation algorithm handling both convex and non-convex theories, that  ...  This paper studies the modularity of quantifier-free interpolation.  ... 
doi:10.1007/978-3-642-31365-3_12 fatcat:tv5qcgd7frfwbcglq7fgne5lta

A Quantifier Elimination Algorithm for Linear Modular Equations and Disequations [chapter]

Ajith K. John, Supratik Chakraborty
2011 Lecture Notes in Computer Science  
We present a layered bit-blasting-free algorithm for existentially quantifying variables from conjunctions of linear modular (bitvector) equations (LMEs) and disequations (LMDs).  ...  Our experiments establish conclusively that our technique significantly outperforms alternative techniques for eliminating quantifiers from systems of LMEs and LMDs in practice.  ...  Since bit-vector arithmetic is the same as modular arithmetic on integers, our algorithm can also be viewed as one for existentially quantifying variables from a Boolean combination of linear modular integer  ... 
doi:10.1007/978-3-642-22110-1_39 fatcat:dpui6tghqvg5tdufnu4h4m7ca4

One quantifier alternation in first-order logic with modular predicates

Manfred Kufleitner, Tobias Walter
2015 RAIRO - Theoretical Informatics and Applications  
Adding modular predicates yields a generalization of first-order logic FO over words.  ...  The fragment Σ 2 consists of first-order formulas in prenex normal form with two blocks of quantifiers starting with an existential block.  ...  Acknowledgements We thank Luc Dartois, Alexander Lauser, and Charles Paperman for several fruitful discussions on modular predicates, we thank Volker Diekert for discussions on the proof of Lemma 5.6,  ... 
doi:10.1051/ita/2014024 fatcat:yor2lwm5f5eqzjpnx3x3xzclsm

Metabolomic Modularity Analysis (MMA) to Quantify Human Liver Perfusion Dynamics

Gautham Sridharan, Bote Bruinsma, Shyam Bale, Anandh Swaminathan, Nima Saeidi, Martin Yarmush, Korkut Uygun
2017 Metabolites  
In addition to cofactor analysis, primary metabolites were quantified using GC-TOF-MS at the West Coast Metabolomics Center (Davis, CA, USA).  ...  As a result, for Liver 1, while only 73 unique metabolites were quantified as SSM, 129 of the 5063 metabolites in the model were denoted as SSM.  ... 
doi:10.3390/metabo7040058 pmid:29137180 pmcid:PMC5746738 fatcat:gibgry3fi5g47btbeiyx5ubrza

Weighing the impact of ICT on modular SMEs

Alessandro Marchetto, Mattia Monga, Andrea Trentini
2007 2007 IEEE International Conference on Exploring Quantifiable IT Yields  
In this paper we propose a method to assess how effective is the information exchange among firm modular units.  ...  We call "modular firm" a network of small interacting firms, exchanging artifacts (atoms) and information (bits) to accomplish a common goal.  ...  Modularization is usually power, since a modular firm can be more flexible and adaptive to market evolution, labor costs fluctuations, etc.  ... 
doi:10.1109/equity.2007.15 fatcat:4ox3a5sfqvbhrltj6oflx4zoim

Identifying, Assigning, and Quantifying Crosscutting Concerns

Marc Eaddy, Alfred Aho, Gail C. Murphy
2007 First International Workshop on Assessment of Contemporary Modularization Techniques (ACoM '07)  
We propose a systematic methodology for identifying which code is related to which concern, and a suite of metrics for quantifying the amount of crosscutting code.  ...  Before we can modularize the crosscutting concerns in our programs to increase software quality, we must first be able to find them.  ...  Conclusion Before we can modularize concerns, we must be able to locate and quantify them.  ... 
doi:10.1109/acom.2007.4 fatcat:u6z2gm7ejncbdohdlda4c5q32i

Modular Scanning FCS quantifies ligand-receptor interactions in live multicellular organisms

Jonas Ries, Rachel Shuizi Yu, Markus Burkhardt, Michael Brand, Petra Schwille
2009 Biophysical Journal  
TR-FRET is a powerful technique for connecting structural dynamics of SERCA with its static crystal structures. 1075-Plat Modular Scanning FCS quantifies ligand-receptor interactions in live multicellular  ...  We were able to quantify the mobility of fibroblast growth factor receptors in cell membranes of living zebrafish embryos and show that Fgfr1 and Fgfr4 have similar binding affinities to the ligand Fgf8  ...  TR-FRET is a powerful technique for connecting structural dynamics of SERCA with its static crystal structures. 1074-Plat 1075-Plat Modular Scanning FCS quantifies ligand-receptor interactions in live  ... 
doi:10.1016/j.bpj.2008.12.1849 fatcat:kgtqvfsfzbecjdipjpnkjiu4tq

Using Neural Pattern Classifiers to Quantify the Modularity of Conflict-Control Mechanisms in the Human Brain

J. Jiang, T. Egner
2013 Cerebral Cortex  
Overall, these findings suggest a hybrid neural architecture of conflict-control that entails both modular (domain specific) and global (domain general) components.  ...  Quantifying the proportion of domainspecific searchlights (capable of decoding only one type of conflict) and domain-general searchlights (capable of decoding both conflict types) in each subject, we found  ...  These data suggest a hybrid architecture of both modular and centralized cognitive control mechanisms.  ... 
doi:10.1093/cercor/bht029 pmid:23402762 pmcid:PMC4051892 fatcat:h33dwqpozvci3o5ef3pnzcuwoa
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