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The complexity of monadic recursion schemes: exponential time bounds

1984
*
Journal of computer and system sciences (Print)
*

We study

doi:10.1016/0022-0000(84)90021-7
fatcat:lel4ewpltzbprgjwjb3vaapofq
*the*computational*complexity**of*decision problems for*the*class X*of**monadic**recursion**schemes*. ...*The*executability problem for a class V*of*very simple*monadic**recursion**schemes*is shown to require deterministic*exponential**time*. ... A*monadic**recursion**scheme*S is said to be AN*EXPONENTIAL**TIME*LOWER*BOUND*FOR*THE*EP In this section we prove that a restricted version*of**the*executability problem for a class g*of*very simple*monadic*...##
###
The complexity of monadic recursion schemes: Executability problems, nesting depth, and applications

1983
*
Theoretical Computer Science
*

*Exponential*

*bounds*are obta ned for

*the*classes

*of*

*monadic*

*recursion*

*schemes*: but polynomial

*bounds*are obtained for t'te classes

*of*total

*monadic*and linear

*monadic*

*recursion*

*schemes*. ... Let YZ be

*the*class

*of*

*monadic*, total

*monadic*or linear

*monadic*

*recursion*schemec;. ...

*Exponential*

*bounds*are obtained for

*the*class

*of*

*monadic*

*recursion*

*schemes*. O(n")

*bounds*are obtained for

*the*classes

*of*total

*monadic*or linear

*monadic*

*recursion*

*schemes*. ...

##
###
On the Hoare theory of monadic recursion schemes

2014
*
Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) - CSL-LICS '14
*

*The*equational theory

*of*

*monadic*

*recursion*

*schemes*is known to be decidable by

*the*result

*of*Sénizergues on

*the*decidability

*of*

*the*problem

*of*DPDA equivalence. ... We investigate

*the*Hoare theory

*of*

*monadic*

*recursion*

*schemes*, that is,

*the*set

*of*valid implications whose conclusions are Hoare assertions and whose premises are

*of*a certain simple form. ... We calculate an

*exponential*upper

*bound*for

*the*running

*time*

*of*

*the*

*recursive*algorithm. ...

##
###
The Hoare Logic of Deterministic and Nondeterministic Monadic Recursion Schemes

2016
*
ACM Transactions on Computational Logic
*

*The*equational theory

*of*deterministic

*monadic*

*recursion*

*schemes*is known to be decidable by

*the*result

*of*Sénizergues on

*the*decidability

*of*

*the*problem

*of*DPDA equivalence. ... We investigate

*the*Hoare theory

*of*

*monadic*

*recursion*

*schemes*, that is,

*the*set

*of*valid implications whose conclusions are Hoare assertions and whose premises are

*of*a certain simple form. ... We calculate an

*exponential*upper

*bound*for

*the*running

*time*

*of*

*the*

*recursive*algorithm. We think

*of*

*the*tree

*of*

*recursive*calls. Let n be

*the*size

*of*

*the*program g. ...

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

2022
*
arXiv
*
pre-print

In this work we prove, under a syntactical constraint called safety, decidability

arXiv:2004.12187v3
fatcat:dgp2l6se7rdvfnvbtc2wehzg4q
*of**the*model-checking problem for*recursion**schemes*against properties defined by alternating B-automata, an extension ... We then exploit this result to show how to compute downward closures*of*languages*of*finite trees recognized by safe*recursion**schemes*. ... automaton (which is equi-expressive with MSO on trees, but less succinct),*the*MSO model-checking problem for*recursion**schemes**of*order n is complete for n-fold*exponential**time*[9] . ...##
###
A Scheme to Verify Services with Unboundedly many Clients using NuSMV
[article]

2018
*
arXiv
*
pre-print

We study model checking

arXiv:1812.00183v1
fatcat:rttnilfkfbeazlokcbn3cnzkla
*of*client - server systems, where*the*servers offer several types*of*services that may depend, at any*time*, on how many clients*of*specific types are active at that*time*. ...*The*MFO sentences throw up a*bound*which can, in turn, be used to*bound**the*state space*of**the*input client - server system, thereby making*the*verification problem decidable. ... Discussion & Future Work We have presented a simple model for client -server systems where*the*number*of*clients is known only at run-*time*and hence unbounded. ...##
###
Page 3756 of Mathematical Reviews Vol. , Issue 86h
[page]

1986
*
Mathematical Reviews
*

*The*authors use executability problems to establish deterministic

*exponential*

*time*lower

*bounds*for

*the*

*complexity*

*of*various decision problems for

*the*class

*of*

*monadic*

*recursion*

*schemes*. ... 86h:68057 {For

*the*entire collection see MR 86d:68001.} Hunt, H. B., Ill (1-SUNYA-C); Rosenkrantz, D. J. (1-SUNYA-C)

*The*

*complexity*

*of*

*monadic*

*recursion*

*schemes*:

*exponential*

*time*

*bounds*. J. Comput. ...

##
###
Recursion Schemes, Collapsible Pushdown Automata and Higher-Order Model Checking
[chapter]

2013
*
Lecture Notes in Computer Science
*

*Recursion*

*schemes*are in essence

*the*simply-typed lambda calculus with

*recursion*, generated from first-order symbols. ... A central theme

*of*

*the*work is

*the*fruitful interplay

*of*ideas between

*the*neighbouring fields

*of*semantics and algorithmic verification. ... Acknowledgements Much

*of*my work presented here is based on collaboration. I am grateful to all my collaborators for their help. Thanks are also due to EPSRC for financial support. ...

##
###
Page 1661 of Mathematical Reviews Vol. , Issue 82d
[page]

1982
*
Mathematical Reviews
*

classes

*of**monadic**recursion**schemes**of*unbounded*complexity*and infinite hierarchies*of**bounded**complexity*classes. ... Simple conditions are found under which a function is a nonreducible upper*bound**of**complexity**of*a*monadic**recursion**scheme*.” ...##
###
Recursion Schemes and Logical Reflection

2010
*
2010 25th Annual IEEE Symposium on Logic in Computer Science
*

In this paper, we prove that higher-order

doi:10.1109/lics.2010.40
dblp:conf/lics/BroadbentCOS10
fatcat:qpkit35y3fb6zc6xo5z4jjw2be
*recursion**schemes*are reflective w.r.t. both modal µ-calculus and*monadic*second order (MSO) logic. ... (Order-n*recursion**schemes*are equi-expressive with order-n CPDA for generating trees.) ... In order to construct t ϕ , we first annotate t with informations on*the*behaviour*of*B on*the*subtrees*of*t. We mark ...##
###
Thin graph classes and polynomial-time approximation schemes
[article]

2017
*
arXiv
*
pre-print

We present a new type

arXiv:1704.00125v1
fatcat:62cftqx65bfq5bdsp6iyqisyfq
*of*graph decompositions (thin systems*of*overlays) generalizing Baker's technique and leading to straightforward polynomial-*time*approximation*schemes*. ... Her technique can be directly extended to various other graph classes, among*the*most general ones*the*graphs avoiding a fixed apex graph as a minor. ... Regarding*the**time**complexity**of**the*algorithms, for all*the*classes*of*graphs that we consider*the*function q is subpolynomial, and thus*the**time**complexity*turns out to be at most O(p(n) + n 1+δ ) for ...##
###
A Complexity Theory for Labeling Schemes
[article]

2018
*
arXiv
*
pre-print

A representation

arXiv:1802.02819v1
fatcat:uy2s2d2m4rg6zfnhlt6noyg46y
*of*a graph from that class is given by*the*set*of*its vertex labels. ... In a labeling*scheme**the*vertices*of*a given graph from a particular class are assigned short labels such that adjacency can be algorithmically determined from these labels. ...*The*three basic quality criteria*of*a labeling*scheme*are*the*label length measured in terms*of**the*number*of*vertices,*the**time*required to determine P from*the*labels called decoding*time*and*the**time*...##
###
Page 2082 of Mathematical Reviews Vol. 53, Issue 6
[page]

1977
*
Mathematical Reviews
*

“In

*the*second part*of**the*paper, adding*the*possibility*of*testing*the*procedure result, a generalization*of**the**monadic**recursive**scheme*is defined. ... As an application,*the*estimation*of**the*lower*bound*on*the**complexity*gap between AND/OR and AND/NOT circuits implementing Boolean mono- tone functions is improved by almost one*exponential*. ...##
###
Page 5150 of Mathematical Reviews Vol. , Issue 2004g
[page]

2004
*
Mathematical Reviews
*

It is shown that there exist sets which are almost complete but not complete (under polynomial-

*time*many-one reductions) for*the*class*of*linear-*exponential**time*computable sets. ... Similar results are obtained for*the*class*of*polynomial-*exponential**time*computable sets. Uwe Schéning (D-ULM-TI; Ulm) 20042:03064 03D15 03B55 03C40 68Q17 Maksimova, L. ...##
###
Page 951 of Mathematical Reviews Vol. 55, Issue 3
[page]

1978
*
Mathematical Reviews
*

Author’s summary: “

*The*equivalence problem for languages accepted by deterministic pushdown automata is shown to be decidable if and only if*the*strong equivalence problem for*monadic**recursion**schemes*... Vincentiu Dumitru (Bucharest) Friedman, Emily P. 6958 Relationships between*monadic**recursion**schemes*and deter- ministic context-free languages. 15th Annual Symposium on Switching and Automata Theory ...
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