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Integer Circuit Evaluation Is PSPACE-Complete

Ke Yang
<span title="">2001</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/p6ovb2qpkfenhmb7mcksobrcxq" style="color: black;">Journal of computer and system sciences (Print)</a> </i> &nbsp;
In this paper we show that the Integer Circuit problem is PSPACE-complete, resolving an open problem posed by McKenzie, Vollmer and Wagner 7].  ...  Wagner 10] introduced the Integer Circuit Evaluation problem.  ...  One of the open problems in their paper is the PSPACE-completeness of the Integer Circuit Evaluation problem.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1006/jcss.2001.1768">doi:10.1006/jcss.2001.1768</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/q7gtaf22ivarngrt7zpn7p64mi">fatcat:q7gtaf22ivarngrt7zpn7p64mi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190305034402/http://pdfs.semanticscholar.org/c58e/32f7ae7b2b98aff91ab10c1a076c0c25d286.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/c5/8e/c58e32f7ae7b2b98aff91ab10c1a076c0c25d286.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1006/jcss.2001.1768"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Integer circuit evaluation is PSPACE-complete

Ke Yang
<i title="IEEE Comput. Soc"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/fvcoh2vdcnbppmicpce3jet6r4" style="color: black;">Proceedings 15th Annual IEEE Conference on Computational Complexity</a> </i> &nbsp;
Wagner (1984, Technical report N/84/52, Friedrich-Schiler-Universität Jena) introduced the integer circuit evaluation problem.  ...  In this paper we show that the integer circuit problem is PSPACEcomplete, resolving an open problem posed by P. McKenzie, H. Vollmer, and  ...  One of the open problems in their paper is the PSPACE-completeness of the integer circuit evaluation problem.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/ccc.2000.856751">doi:10.1109/ccc.2000.856751</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/coco/Yang00.html">dblp:conf/coco/Yang00</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/wi5mlzoq7rhk3alezksdg2jbqa">fatcat:wi5mlzoq7rhk3alezksdg2jbqa</a> </span>
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Relations and Equivalences Between Circuit Lower Bounds and Karp-Lipton Theorems

Lijie Chen, Dylan M. McKay, Cody D. Murray, R. Ryan Williams, Michael Wagner
<span title="2019-07-16">2019</span> <i > <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/fvcoh2vdcnbppmicpce3jet6r4" style="color: black;">Computational Complexity Conference</a> </i> &nbsp;
A frontier open problem in circuit complexity is to prove P NP ⊂ SIZE[n k ] for all k; this is a necessary intermediate step towards NP ⊂ P /poly .  ...  That is, if NP ⊂ SIZE[n k ] for all k, then for all C ∈ {⊕P, PP, PSPACE, EXP}, C ⊂ P /poly implies C ⊂ i.o.-NP /n ε for all ε > 0. Note that unconditionally, the collapses are only to MA and not NP.  ...  Acknowledgements Part of this work was completed while three of the authors were visiting the Simons Institute at UC Berkeley, as part of the program on Lower Bounds in Computational Complexity.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/lipics.ccc.2019.30">doi:10.4230/lipics.ccc.2019.30</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/coco/ChenMMW19.html">dblp:conf/coco/ChenMMW19</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/zeygcjns65bbnadktltfjkhtwy">fatcat:zeygcjns65bbnadktltfjkhtwy</a> </span>
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The complexity of membership problems for circuits over sets of integers

Stephen Travers
<span title="">2006</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/elaf5sq7lfdxfdejhkqbtz6qoq" style="color: black;">Theoretical Computer Science</a> </i> &nbsp;
As another result, evaluating { − , +}-circuits is shown to be P-complete for the integers and PSPACE-complete for the natural numbers.  ...  in the subset of integers produced at the output of a {∪, +, ×}-circuit is NEXPTIME-complete, whereas it is PSPACE-complete for the natural numbers.  ...  Acknowledgments The author is grateful to Klaus W.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.tcs.2006.08.017">doi:10.1016/j.tcs.2006.08.017</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/3uvp4ax5fba33a6q7zqtvykbhm">fatcat:3uvp4ax5fba33a6q7zqtvykbhm</a> </span>
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Satisfiability of algebraic circuits over sets of natural numbers

Christian Glaßer, Christian Reitwießner, Stephen Travers, Matthias Waldherr
<span title="">2010</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/lx7dev2le5anbg6oarljwh7lie" style="color: black;">Discrete Applied Mathematics</a> </i> &nbsp;
In particular, we prove that testing satisfiability for {∩, +, ×}-circuits already is undecidable. In contrast to this, the satisfiability for {∪, +, ×}circuits is decidable in PSPACE.  ...  Our work shows that satisfiability problems capture a wide range of complexity classes like NL, P, NP, PSPACE, and beyond.  ...  Evaluate the circuit using the same algorithm as in Theorem 2.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.dam.2010.04.001">doi:10.1016/j.dam.2010.04.001</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ogjdefrwk5cwtd4mmzryyyt6ru">fatcat:ogjdefrwk5cwtd4mmzryyyt6ru</a> </span>
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Satisfiability of Algebraic Circuits over Sets of Natural Numbers [chapter]

Christian Glaßer, Christian Reitwießner, Stephen Travers, Matthias Waldherr
<span title="">2007</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
In particular, we prove that testing satisfiability for {∩, +, ×}-circuits already is undecidable. In contrast to this, the satisfiability for {∪, +, ×}circuits is decidable in PSPACE.  ...  Our work shows that satisfiability problems capture a wide range of complexity classes like NL, P, NP, PSPACE, and beyond.  ...  Evaluate the circuit using the same algorithm as in Theorem 2.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-540-77050-3_21">doi:10.1007/978-3-540-77050-3_21</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/f3omcobrkjg5lkk6ucwgvre5x4">fatcat:f3omcobrkjg5lkk6ucwgvre5x4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170829095641/http://www1.pub.informatik.uni-wuerzburg.de/pub/TRs/glretrwa07.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/95/05/950557000d1ec8d72605279efcac21cde347eb86.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-540-77050-3_21"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Functions computable in polynomial space

Matthias Galota, Heribert Vollmer
<span title="">2005</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/joe2ngto45hbnl3pncnesnq344" style="color: black;">Information and Computation</a> </i> &nbsp;
We show that the class of functions f computable as just described is exactly the class FPSPACE of integer-valued functions computable by polynomial-space Turing machines.  ...  Along the way we obtain characterizations of FPSPACE in terms of arithmetic circuits and straight-line programs.  ...  nonzero, is complete for PSPACE under first-order projections. .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.ic.2005.02.002">doi:10.1016/j.ic.2005.02.002</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/dc5yealwpbg2bjllqohia3b3tm">fatcat:dc5yealwpbg2bjllqohia3b3tm</a> </span>
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Complexity of finite-horizon Markov decision process problems

Martin Mundhenk, Judy Goldsmith, Christopher Lusena, Eric Allender
<span title="2000-07-01">2000</span> <i title="Association for Computing Machinery (ACM)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/r72grtxx6jad5hjzl7fxcunwhi" style="color: black;">Journal of the ACM</a> </i> &nbsp;
The long term stationary policy evaluation problem for compressed UMDPs is PSPACE-complete. Proof.  ...  A standard complete problem for this class is the circuit value problem CVP: given a Boolean circuit and an input, does the circuit output a 1?  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/347476.347480">doi:10.1145/347476.347480</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/dko66dgsi5cfvph4uzmtkyppqm">fatcat:dko66dgsi5cfvph4uzmtkyppqm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20050317203325/http://ftp.cs.rutgers.edu:80/pub/allender/goldsmith.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/c4/2b/c42be3de7972666e116fbacb42a91f031b3bc662.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/347476.347480"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

Page 7540 of Mathematical Reviews Vol. , Issue 2002J [page]

<span title="">2002</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
= x; or x; = X;) of dimension at least log(a/s)/logn.” 2002):68036 68Q17 Yang, Ke (1-CMU-C; Pittsburgh, PA) Integer circuit evaluation is PSPACE-complete.  ...  In this paper we show that the integer circuit problem is PSPACE-complete, resolving an open problem posed by P. McKenzie, H. Vollmer and K. W.  ... 
<span class="external-identifiers"> </span>
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Valiant?s model and the cost of computing integers

Pascal Koiran
<span title="">2005</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/t46w5lpc3ngnfmzil33zdjjrp4" style="color: black;">Computational Complexity</a> </i> &nbsp;
For the second sequence, a proof would imply a superpolynomial lower bound for the permanent or P = PSPACE.  ...  Let τ (n) be the minimum number of arithmetic operations required to build the integer n ∈ N from the constants 1 and 2.  ...  The basic idea is quite simple: if an integer polynomial can be evaluated efficiently, its values at integer points are integers of low cost.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s00037-004-0186-2">doi:10.1007/s00037-004-0186-2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/tzk25y6kgbbhpcq2dmsbeaceiq">fatcat:tzk25y6kgbbhpcq2dmsbeaceiq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170809105047/http://perso.ens-lyon.fr/pascal.koiran/Publis/tau.springer.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/0c/a1/0ca1694d3e7449f4967e2b251f0b99e6e18ec492.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s00037-004-0186-2"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Decidable Membership Problems for Finite Recurrent Systems over Sets of Naturals [chapter]

Daniel Meister
<span title="">2005</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
We will show completeness results for the complexity classes NL, NP and PSPACE. M. Liśkiewicz and R. Reischuk (Eds.): FCT 2005, LNCS 3623, pp. 80-91, 2005.  ...  The last component of a generated n-tuple is the output of one step, and the union of all outputs is the set defined by the system.  ...  The idea to study finite recurrent systems was the result of a discussion with Klaus Wagner when a lot of people at Würzburg were studying membership problems for arithmetic circuits.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/11537311_8">doi:10.1007/11537311_8</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/5wdqt35wrzer5bzkstst4ska4m">fatcat:5wdqt35wrzer5bzkstst4ska4m</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170811163258/https://esp.mit.edu/download/ea6ef2a55b8219b543fa09130f64325d/M3175_Decidable_Membership_Problems_for_Finite_Recurrent_Systems_over_Sets_of_Naturals.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/c2/e7/c2e71f01b6ffe18b4d13b36736d212a7a9365e45.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/11537311_8"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

VPSPACE and a Transfer Theorem over the Reals

Pascal Koiran, Sylvain Perifel
<span title="2009-09-25">2009</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/t46w5lpc3ngnfmzil33zdjjrp4" style="color: black;">Computational Complexity</a> </i> &nbsp;
Our main theorem is that if (uniform, constant-free) VPSPACE families can be evaluated efficiently then the class PAR R of decision problems that can be solved in parallel polynomial time over the real  ...  Roughly speaking, a family of polynomials is in VPSPACE if its coefficients can be computed in polynomial space.  ...  A typical example of an evaluation problem is the evaluation of the permanent of a matrix, and it is well known since Valiant (1979) that the permanent family is complete for the class VNP of "easily  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s00037-009-0269-1">doi:10.1007/s00037-009-0269-1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/jzuyeomoevdavavlfgskxkaqw4">fatcat:jzuyeomoevdavavlfgskxkaqw4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20080425153937/http://perso.ens-lyon.fr/pascal.koiran/Publis/vpspace.long.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/c7/8d/c78d4c573ae6b4fb7481a84895e691fe0eda98fe.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s00037-009-0269-1"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

The pervasive reach of resource-bounded Kolmogorov complexity in computational complexity theory

Eric Allender, Michal Koucký, Detlef Ronneburger, Sambuddha Roy
<span title="">2011</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/p6ovb2qpkfenhmb7mcksobrcxq" style="color: black;">Journal of computer and system sciences (Print)</a> </i> &nbsp;
We continue an investigation into resource-bounded Kolmogorov complexity [ABK + 06], which highlights the close connections between circuit complexity and Levin's time-bounded Kolmogorov complexity measure  ...  The main theorems that we provide using this new approach to resource-bounded Kolmogorov complexity are: • A complete set (RKNt) for NEXP/poly defined in terms of strings of high Kolmogorov complexity.  ...  The circuit evaluates to 1 on an input x, and we say that C(x) = 1, if there is some assignment of truth values to the choice-gates that makes the circuit evaluate to 1.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.jcss.2010.06.004">doi:10.1016/j.jcss.2010.06.004</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/zmhc3ae4pne2zbntlzyhd2kngi">fatcat:zmhc3ae4pne2zbntlzyhd2kngi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170808112437/http://iuuk.mff.cuni.cz/~koucky/papers/perk.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/8f/7f/8f7f4654868e48fbc4f8ff2e2fa19f59f5cf8a8e.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.jcss.2010.06.004"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Groups with ALOGTIME-Hard Word Problems and PSPACE-Complete Circuit Value Problems

Laurent Bartholdi, Michael Figelius, Markus Lohrey, Armin Weiß, Shubhangi Saraf
<span title="2020-07-17">2020</span> <i title="Schloss Dagstuhl - Leibniz-Zentrum für Informatik"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/fvcoh2vdcnbppmicpce3jet6r4" style="color: black;">Computational Complexity Conference</a> </i> &nbsp;
For some of these groups (including Grigorchuk's group and Thompson's groups) we prove that the circuit value problem (which is equivalent to the circuit evaluation problem) is PSPACE-complete.  ...  problem of certain non-solvable groups: for a large class of non-solvable infinite groups, including in particular free groups, Grigorchuk's group and Thompson's groups, we prove that their word problem is  ...  CVP(G Z) is hard for the class ∀LEAF(WP(G/Z)). In particular, if Z = 1, then CVP(G Z) is complete for ∀LEAF(WP(G)). PSPACE-complete circuit value problems.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/lipics.ccc.2020.29">doi:10.4230/lipics.ccc.2020.29</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/coco/BartholdiFLW20.html">dblp:conf/coco/BartholdiFLW20</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/euwyp4j3tramrfrzguxmauk3re">fatcat:euwyp4j3tramrfrzguxmauk3re</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20201212022925/https://drops.dagstuhl.de/opus/volltexte/2020/12581/pdf/LIPIcs-CCC-2020-29.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/82/e6/82e62cf9eb33f6bad275254712e99596cb715496.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/lipics.ccc.2020.29"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

The Complexity of the Path-following Solutions of Two-dimensional Sperner/Brouwer Functions [article]

Paul W. Goldberg
<span title="2015-06-16">2015</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
There are a number of results saying that for certain "path-following" algorithms that solve PPAD-complete problems, the solution obtained by the algorithm is PSPACE-complete to compute.  ...  Here we show that it is PSPACE-complete to compute this specific solution, together with a similar result for the computation of the path-following solution of two-dimensional discrete Brouwer functions  ...  also PSPACE-complete to compute.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1506.04882v1">arXiv:1506.04882v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/spqpiirqrfcafowuxlmynpb76m">fatcat:spqpiirqrfcafowuxlmynpb76m</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200901013308/https://arxiv.org/pdf/1506.04882v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/5b/12/5b12368c27a81d4acf55d5cdc9f2eae6df9c1cf6.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1506.04882v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>
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