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The Diagonal Problem for Higher-Order Recursion Schemes is Decidable [article]

Lorenzo Clemente and Paweł Parys and Sylvain Salvati and Igor Walukiewicz
2016 arXiv   pre-print
We show decidability of the diagonal problem for schemes. This result has several interesting consequences.  ...  A non-deterministic recursion scheme recognizes a language of finite trees. This very expressive model can simulate, among others, higher-order pushdown automata with collapse.  ...  From point 3 of Lemma 5.13 it follows that tr cum (D ′ ) is mergeequivalent to P , what finishes the proof. Theorem 3. 1 . 1 The diagonal problem for higher-order recursion schemes is decidable.  ... 
arXiv:1605.00371v1 fatcat:oxtwnm4fqrbgxlz66cyabmvumq

The Diagonal Problem for Higher-Order Recursion Schemes is Decidable

Lorenzo Clemente, Paweł Parys, Sylvain Salvati, Igor Walukiewicz
2016 Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science - LICS '16  
The diagonal problem for schemes is to decide whether Diag Σ (S) holds for a given scheme S and a set Σ. Theorem 3.1. The diagonal problem for higher-order recursion schemes is decidable. Proof.  ...  Our main result is a procedure for solving the diagonal problem for higher-order schemes. This is a missing ingredient to obtain several new decidability results for this model.  ...  A higher-order recursion scheme with states (HORSS) is a triple H = (Q, (qinit , Ainit ), R), where Q is a finite set of control states, (qinit , Ainit ) is the initial process with qinit the initial control  ... 
doi:10.1145/2933575.2934527 dblp:conf/lics/ClementePSW16 fatcat:5yqekesdrbg7dckalqb3i7iyom

Cost Automata, Safe Schemes, and Downward Closures [article]

David Barozzini, Lorenzo Clemente, Thomas Colcombet, Paweł Parys
2022 arXiv   pre-print
In this work we prove, under a syntactical constraint called safety, decidability of the model-checking problem for recursion schemes against properties defined by alternating B-automata, an extension  ...  Higher-order recursion schemes are an expressive formalism used to define languages of finite and infinite ranked trees.  ...  The diagonal problem for languages of finite words recognized by recursion schemes is decidable [23, 24, 25] .  ... 
arXiv:2004.12187v3 fatcat:dgp2l6se7rdvfnvbtc2wehzg4q

Cost Automata, Safe Schemes, and Downward Closures

David Barozzini, Lorenzo Clemente, Thomas Colcombet, Paweł Parys, Emanuela Merelli, Artur Czumaj, Anuj Dawar
2020 International Colloquium on Automata, Languages and Programming  
In this work we prove, under a syntactical constraint called safety, decidability of the model-checking problem for recursion schemes against properties defined by alternating B-automata, an extension  ...  Higher-order recursion schemes are an expressive formalism used to define languages of possibly infinite ranked trees.  ...  By Theorem 4.5 and Lemma 4.8, all we need to do is to show that the diagonal problem is decidable for languages recognized by safe recursion schemes, that is, that given a safe recursion scheme G and a  ... 
doi:10.4230/lipics.icalp.2020.109 dblp:conf/icalp/BarozziniCCP20 fatcat:kk2gv3niuvdl3iyq2dptfffglq

The Complexity of the Diagonal Problem for Recursion Schemes

Pawel Parys, Marc Herbstritt
2018 Foundations of Software Technology and Theoretical Computer Science  
We establish the complexity of the diagonal problem for schemes: given a set of letters A and a scheme G, is it the case that for every number n the scheme accepts a word (a tree) in which every letter  ...  We prove that this problem is (m−1)-EXPTIME-complete for word-recognizing schemes of order m, and m-EXPTIME-complete for tree-recognizing schemes of order m.  ...  The diagonal problem for tree-recognizing order-m schemes is to decide whether Diag A (L(G)) holds, given a scheme G of order at most m and a set A.  ... 
doi:10.4230/lipics.fsttcs.2017.45 dblp:conf/fsttcs/Parys17 fatcat:vultckgqabh7tbpjepoirksrxi

Higher-Order Model Checking: An Overview

Luke Ong
2015 2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science  
Higher-order model checking is about the model checking of trees generated by recursion schemes. The past fifteen years or so have seen considerable progress in both theory and practice.  ...  Because the trees generated by recursion schemes are computation trees of higher-order functional programs, higherorder model checking provides a foundation for model checkers of such programming languages  ...  Acknowledgements: The author is grateful to Takeshi Tsukada for helpful comments on the paper.  ... 
doi:10.1109/lics.2015.9 dblp:conf/lics/Ong15 fatcat:55bfxqlkuzhbtgmzc32m46ooku

The p-T-degrees of the recursive sets: lattice embeddings, extensions of embeddings and the two-quantifier theory

Richard A. Shore, Theodore A. Slaman
1992 Theoretical Computer Science  
The situation for the p-time many-one degrees is quite different. We decide the extension of the embedding problem (differently than for R") but not the t/3-theory.  ...  We also generalize the density type results of Ladner (1975) and many others to settle the full extension of the embedding problem for R,.,.  ...  In this scheme the typical (delayed) diagonalization constructions for Rp_r might well be called recursive.  ... 
doi:10.1016/0304-3975(92)90078-t fatcat:bpn3g2vl2rfs3ezp6umgqbavty

Page 3359 of Mathematical Reviews Vol. , Issue 84h [page]

1984 Mathematical Reviews  
Ullman suggested the ‘iteration’ method. The main problem found in these methods is that of thediagonal terms’. After the publication of M. H.  ...  Finally, we derive that recursion on higher types induces an infinite hierarchy of control structures by proving that level-n schemes are strictly less powerful than level-(n+ 1) schemes.”  ... 

General Decidability Results for Asynchronous Shared-Memory Programs: Higher-Order and Beyond [chapter]

Rupak Majumdar, Ramanathan S. Thinniyam, Georg Zetzsche
2021 Lecture Notes in Computer Science  
We show that under mild assumptions, surprisingly, safety and termination verification of asynchronous programs with handlers from a language class are decidable iff emptiness is decidable for the underlying  ...  Our results close the decidability frontier for asynchronous programs.  ...  The diagonal problem was then shown to be decidable for higher-order pushdown automata [15] and then for word schemes [7] .  ... 
doi:10.1007/978-3-030-72016-2_24 fatcat:isvi7y2cgnc5bjaxzkey77eshm

Unboundedness and downward closures of higher-order pushdown automata

Matthew Hague, Jonathan Kochems, C.-H. Luke Ong
2016 SIGPLAN notices  
We show the diagonal problem for higher-order pushdown automata (HOPDA), and hence the simultaneous unboundedness problem, is decidable.  ...  Both of these consequences play an important rôle in verifying concurrent higher-order programs expressed as HOPDA or safe higher-order recursion schemes.  ...  When these recursion schemes satisfy a syntactical condition called safety, a restriction of CPDA called higher-order pushdown automata (HOPDA or n-PDA for order-n HOPDA) is sufficient [22, 30] .  ... 
doi:10.1145/2914770.2837627 fatcat:ttceblejtndlbhctixakjbjfai

Unboundedness and downward closures of higher-order pushdown automata

Matthew Hague, Jonathan Kochems, C.-H. Luke Ong
2016 Proceedings of the 43rd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages - POPL 2016  
We show the diagonal problem for higher-order pushdown automata (HOPDA), and hence the simultaneous unboundedness problem, is decidable.  ...  Both of these consequences play an important rôle in verifying concurrent higher-order programs expressed as HOPDA or safe higher-order recursion schemes.  ...  When these recursion schemes satisfy a syntactical condition called safety, a restriction of CPDA called higher-order pushdown automata (HOPDA or n-PDA for order-n HOPDA) is sufficient [22, 30] .  ... 
doi:10.1145/2837614.2837627 dblp:conf/popl/HagueKO16 fatcat:euqumz7dafah7g5d7gp36lxk3a

Mixed Precision Fermi-Operator Expansion on Tensor Cores From a Machine Learning Perspective [article]

Joshua Finkelstein, Justin Smith, Susan M. Mniszewski, Kipton Barros, Christian F. A. Negre, Emanuel H. Rubensson, Anders M. N. Niklasson
2021 arXiv   pre-print
The second-order recursive Fermi-operator scheme is formulated in terms of a generalized, differentiable deep neural network structure, which solves the quantum mechanical electronic structure problem.  ...  We present a second-order recursive Fermi-operator expansion scheme using mixed precision floating point operations to perform electronic structure calculations using tensor core units.  ...  For smaller problems, the construction of the density matrix with direct diagonalization is typically much faster. C.  ... 
arXiv:2101.06385v1 fatcat:7nvdjjisvfgsnm5stt5f575ebe

Synthesis of Recursive Digital Filters with Finite Word Length: Problems and their Solutions

V.A. Lesnikov, T.V. Naumovich, A.V. Chastikov
2019 Problems of advanced micro- and nanoelectronic systems development  
Therefore, it is necessary to either increase the bit depth or change the structural scheme.  ...  It is proposed to generate structural schemes by this nature, based on the revealed algebraic features of the matrix description of structures.  ...  The problem is to determine the maximum degree of zeros for this structure. VII.  ... 
doi:10.31114/2078-7707-2019-3-46-53 fatcat:zwntj65dy5ailpsr27adywcigy

General Decidability Results for Asynchronous Shared-Memory Programs: Higher-Order and Beyond [article]

Rupak Majumdar, Ramanathan S. Thinniyam, Georg Zetzsche
2022 arXiv   pre-print
As a main consequence, we show decidability of safety, termination and boundedness verification for higher-order asynchronous programs -- such as OCaml programs using Lwt -- and undecidability of liveness  ...  We show that under mild assumptions, surprisingly, safety and termination verification of asynchronous programs with handlers from a language class are decidable iff emptiness is decidable for the underlying  ...  The diagonal problem was then shown to be decidable for higher-order pushdown automata [HKO16] and then for word schemes [CPSW16] .  ... 
arXiv:2101.08611v3 fatcat:sdvr72kwyjctjo7cf2qkuidjvy

Degrees of Unsolvability: A Tutorial [chapter]

Stephen G. Simpson
2015 Lecture Notes in Computer Science  
Given a problem P , one associates to P a degree of unsolvability, i.e., a quantity which measures the amount of algorithmic unsolvability which is inherent in P .  ...  This model is a rigorous implementation of Kolmogorov's nonrigorous 1932 interpretation of intuitionism as a "calculus of problems."  ...  We feel that, among various interpretations of intuitionistic mathematics, our interpretation in terms of the Muchnik topos stands out because of its relationship to the ideas of Kolmogorov, Medvedev,  ... 
doi:10.1007/978-3-319-20028-6_9 fatcat:l52kiot3y5dafoqwsgp5s3d4ta
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