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The complexity of monadic recursion schemes: exponential time bounds

H.B. Hunt, D.J. Rosenkrantz
1984 Journal of computer and system sciences (Print)  
We study 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  ... 
doi:10.1016/0022-0000(84)90021-7 fatcat:lel4ewpltzbprgjwjb3vaapofq

The complexity of monadic recursion schemes: Executability problems, nesting depth, and applications

H.B. Hunt, D.J. Rosenkrantz
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.  ... 
doi:10.1016/0304-3975(83)90091-9 fatcat:owyzkwsmvja6revt6hh5g5jyga

On the Hoare theory of monadic recursion schemes

Konstantinos Mamouras
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.  ... 
doi:10.1145/2603088.2603157 dblp:conf/csl/Mamouras14 fatcat:oivse44ndzg5nok5t7nflq54ha

The Hoare Logic of Deterministic and Nondeterministic Monadic Recursion Schemes

Konstantinos Mamouras
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.  ... 
doi:10.1145/2835491 fatcat:avxpvu2hmzghnaviey4pesq5ie

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  ...  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] .  ... 
arXiv:2004.12187v3 fatcat:dgp2l6se7rdvfnvbtc2wehzg4q

A Scheme to Verify Services with Unboundedly many Clients using NuSMV [article]

S Sheerazuddin, S Anand, R S Anish Badhri
2018 arXiv   pre-print
We study model checking 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.  ... 
arXiv:1812.00183v1 fatcat:rttnilfkfbeazlokcbn3cnzkla

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]

Luke Ong
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.  ... 
doi:10.1007/978-3-642-37064-9_3 fatcat:vmzogjyskfahbeklhyssyajvuy

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

Christopher H. Broadbent, Arnaud Carayol, C.-H. Luke Ong, Olivier Serre
2010 2010 25th Annual IEEE Symposium on Logic in Computer Science  
In this paper, we prove that higher-order 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  ... 
doi:10.1109/lics.2010.40 dblp:conf/lics/BroadbentCOS10 fatcat:qpkit35y3fb6zc6xo5z4jjw2be

Thin graph classes and polynomial-time approximation schemes [article]

Zdeněk Dvořák
2017 arXiv   pre-print
We present a new type 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  ... 
arXiv:1704.00125v1 fatcat:62cftqx65bfq5bdsp6iyqisyfq

A Complexity Theory for Labeling Schemes [article]

Maurice Chandoo
2018 arXiv   pre-print
A representation 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  ... 
arXiv:1802.02819v1 fatcat:uy2s2d2m4rg6zfnhlt6noyg46y

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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