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Linear time hierarchies for a functional language machine model [chapter]

Eva Rose
1996 Lecture Notes in Computer Science  
We consider the Categorical Abstract Machine (CAM), a canonical machine model for implementing higher order functional languages.  ...  In STOC 93, Jones sketched the existence of a hierarchy within problems decidable in linear time by a rst-order functional language based on tree-structured data (F), as well as for an extension of that  ...  Thanks are due to my supervisor, Neil Jones, for introducing me to the subject and for fruitful discussions along.  ... 
doi:10.1007/3-540-61055-3_45 fatcat:qih4tzizpjggxf6aszprjtc6km

Linear-time hierarchies for a functional language machine model

Eva Rose
1998 Science of Computer Programming  
In STOC 1993, Jones showed the existence of a hierarchy within problems decidable in linear time by a canonical first-order functional language based on tree-structured data (F), as well as for an extension  ...  In this paper, we prove the existence of a linear-time hierarchy for an authentic and realistic intermediate "machine" language featuring higher order constructs: the Categorical Abstract Machine.  ...  Acknowledgements This work started as a student project supervised by Neil Jones.  ... 
doi:10.1016/s0167-6423(97)00032-4 fatcat:btmtorijgnbltaoqz7we5p6zkq

Complete sets and the polynomial-time hierarchy

Celia Wrathall
1976 Theoretical Computer Science  
Usiblg this result, a sequence of camp' :te sets for the hierarchy is exhibited..  ...  New prc;ofs of two properties of the polynomial-time hierarchy are given. The classes in the hierarchy are characterized using polynomially bounded quantifiers.  ...  The model for the computation of these functions is a Turing machine with two-way input, multiple work tapes to which the space bound applies, and a one-way output tape.  ... 
doi:10.1016/0304-3975(76)90062-1 fatcat:ohc4jzcmd5f43ir3zb6jddwsqe

Page 1428 of Mathematical Reviews Vol. , Issue 2000b [page]

2000 Mathematical Reviews  
Summary: “We consider a model of analog computation that can recognize various languages in real time.  ...  “We relate this model to other models of analog computation; in particular, it can be seen as a real-time, constant-space, off-line version of Blum, Shub and Smale’s real-valued machines.” 2000b:68068  ... 

Page 4266 of Mathematical Reviews Vol. , Issue 83j [page]

1983 Mathematical Reviews  
The next three sections deal with the hierarchy theorems (one for space and one for time), relations among complexity measures and translational lemmas in connection with nondeterministic hierarchies.  ...  The next chapter deals with the Chomsky hierarchy presenting the equivalences between regular grammars and finite automata, between type 0 grammars and Turing machines as well as between linear bounded  ... 

Page 5683 of Mathematical Reviews Vol. , Issue 99h [page]

1999 Mathematical Reviews  
Chantal Berline (F-PARIS7-ML; Paris) 99h:68027 68N15 68Q05 68Q15 68Q55 Rose, Eva (F-ENSLY-IP; Lyon) Linear-time hierarchies for a functional language machine model.  ...  In this paper, we prove the existence of a linear-time hierarchy for an authentic and realistic intermediate ‘machinelanguage fea- turing higher-order constructs: the categorical abstract machine.  ... 

The Power of Extra Analog Neuron [chapter]

Jiří Šíma
2014 Lecture Notes in Computer Science  
(ξ) = 1 for ξ ≥ 0 0 for ξ < 0 Heaviside function 2. analog-state units with y j ∈ [0, 1] (briefly analog neurons) σ L (ξ) =    1 for ξ ≥ 1 ξ for 0 < ξ < 1 0 for ξ ≤ 0 saturated-linear function σ S (  ...  : finite automaton (Minsky, 1967) 2. rational weights: Turing machine (Siegelmann, Sontag, 1995) polynomial time ≡ complexity class P (with the saturated-linear activation function) depends on the  ...  If every series ∞ k=0 b k a k ∈ C with all b k ∈ B is eventually quasi-periodic, then L(R) accepted by R is a regular language.  ... 
doi:10.1007/978-3-319-13749-0_21 fatcat:2cu4sojsubgtbcshg6n3e2p7ue

Native Chemical Computation. A Generic Application of Oscillating Chemistry Illustrated With the Belousov-Zhabotinsky Reaction. A Review

Marta Dueñas-Díez, Juan Pérez-Mercader
2021 Frontiers in Chemistry  
If so, at what levels in the hierarchy of computing complexity?  ...  Sensitive Language and rejecting words outside the language.  ...  ACKNOWLEDGMENTS We thank REPSOL S.A. for their continued support.  ... 
doi:10.3389/fchem.2021.611120 pmid:34046394 pmcid:PMC8144498 fatcat:2xtxhr2ny5g4zoljsqlf62tbde

On the Computational Complexity of MapReduce [article]

Benjamin Fish and Jeremy Kun and Ádám Dániel Lelkes and Lev Reyzin and György Turán
2015 arXiv   pre-print
In addition, we prove that, conditioned on a variant of the Exponential Time Hypothesis, there are strict hierarchies within MRC so that increasing the number of rounds or the amount of time per processor  ...  In this paper we study MapReduce computations from a complexity-theoretic perspective. First, we formulate a uniform version of the MRC model of Karloff et al. (2010).  ...  Acknowledgements We thank Howard Karloff and Benjamin Moseley for helpful discussions.  ... 
arXiv:1410.0245v2 fatcat:bivfh5pkwnbztjqladsaiic6me

Alternating Hierarchies for Time-Space Tradeoffs [article]

Chris Pollett, Eric Miles
2008 arXiv   pre-print
linear time hierarchy.  ...  By considering restrictions on the size of the universal quantifiers in the linear time hierarchy, this paper refines Nepomnjascii's result to give a sub- hierarchy, Eu-LinH, of the linear time hierarchy  ...  in the linear time hierarchy, LinH.  ... 
arXiv:0801.1307v1 fatcat:2s62cln53fcbff4udv72txowxa

Space Hierarchy Results for Randomized Models

Jeff Kinne, Dieter Van Melkebeek, Marc Herbstritt
2008 Symposium on Theoretical Aspects of Computer Science  
Previous works on hierarchy and separation theorems for such models focused on time as the resource. We obtain tighter results with space as the resource. Our main theorems are the following.  ...  We prove space hierarchy and separation results for randomized and other semantic models of computation with advice.  ...  Acknowledgments We thank Scott Diehl for many useful discussions, in particular pertaining to the proof of Theorem 1.2. We also thank the anonymous reviewers for their time and suggestions.  ... 
doi:10.4230/lipics.stacs.2008.1363 dblp:conf/stacs/KinneM08 fatcat:4gzozyaomrgorjd3vckffdpuge

Constant time factors do matter

Neil D. Jones
1993 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing - STOC '93  
Language I ↑ allows calls to the language's own interpretation function, and even to its running time function (without the usual high costs for nested levels of interpretation).  ...  Second, a problem is exhibited which is complete for the nondeterministic linear time sets NLIN with respect to a natural notion of deterministic linear-time reduction.  ...  Acknowledgements Thanks are given to Henk Barendregt, John Case, Yuri Gurevich, Joel Seiferas, Dieter Spreen, and the programming language research groups at the Universities of Copenhagen and Aarhus.  ... 
doi:10.1145/167088.167244 dblp:conf/stoc/Jones93 fatcat:qaqjcqd2z5fpdjyppfjz5fijhm

Book Review: Deep Learning

Kwang Gi Kim
2016 Healthcare Informatics Research  
Deep learning is a form of machine learning that enables computers to learn from experience and understand the world in terms of a hierarchy of concepts.  ...  partition function, approximate inference, and deep generative models.  ...  Confronting the Partition Function In this chapter, the authors describe techniques used for training and evaluating models that have intractable parti-tion functions. Chapter 19.  ... 
doi:10.4258/hir.2016.22.4.351 pmcid:PMC5116548 fatcat:oz5b4rswyfg5fgfhy4ya2u6qhy

Page 3349 of Mathematical Reviews Vol. , Issue 2001E [page]

2001 Mathematical Reviews  
As an example we give a problem complete for non-deterministic linear time under deterministic linear-time reductions.  ...  In particular, we prove several time hierarchy theorems for deterministic and non-deterministic time complexity which show that, in contrast with Turing machines, constant factors do matter in this framework  ... 

Hierarchical State Machines [chapter]

Mihalis Yannakakis
2000 Lecture Notes in Computer Science  
Hierarchy is a useful construct in many modeling formalisms and tools for software design, requirements and testing.  ...  .), and algorithmic problems in the analysis of hierarchical machines to check for their properties.  ...  In the case of basic FSM's, checking a model M for a formula φ in branching time logic CTL is easier than LTL: it can be done in time O(|M ||φ|), i.e. linear in both the size of the model and the specification  ... 
doi:10.1007/3-540-44929-9_24 fatcat:n7ukehqe65f6palzi25ynu5tea
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