Editing EXPSPACE (section)

== Examples of problems ==

=== Formal languages ===
An example of an {{Sans-serif|EXPSPACE-complete}} problem is the problem of recognizing whether two [[regular expression]]s represent different languages, where the expressions are limited to four operators: union, [[concatenation]], the [[Kleene star]] (zero or more copies of an expression), and squaring (two copies of an expression).<ref>Meyer, A.R. and [[Larry Stockmeyer|L. Stockmeyer]]. [https://people.csail.mit.edu/meyer/rsq.pdf The equivalence problem for regular expressions with squaring requires exponential space]. ''13th IEEE Symposium on Switching and Automata Theory'', Oct 1972, pp.125&ndash;129.</ref>

=== Logic ===
Alur and Henzinger extended [[linear temporal logic]] with times (integer) and prove that the validity problem of their logic is EXPSPACE-complete.<ref>{{Cite journal|last1=Alur|first1=Rajeev|last2=Henzinger|first2=Thomas A.|date=1994-01-01|title=A Really Temporal Logic|journal=J. ACM|volume=41|issue=1|pages=181–203|doi=10.1145/174644.174651|issn=0004-5411|doi-access=free}}</ref>

Reasoning in the first-order theory of the real numbers with +, ×, = is in EXPSPACE and was conjectured to be EXPSPACE-complete in 1986.<ref>{{Cite journal |last=Ben-Or |first=Michael |last2=Kozen |first2=Dexter |last3=Reif |first3=John |date=1986-04-01 |title=The complexity of elementary algebra and geometry |url=https://www.sciencedirect.com/science/article/pii/0022000086900292 |journal=Journal of Computer and System Sciences |volume=32 |issue=2 |pages=251–264 |doi=10.1016/0022-0000(86)90029-2 |issn=0022-0000}}</ref>

=== Petri nets ===
The coverability problem for [[Petri Nets]] is {{Sans-serif|EXPSPACE}}-complete.<ref>{{cite journal | 
  author = Charles Rackoff |
  title = The covering and boundedness problems for vector addition systems |
  journal = Theoretical Computer Science |
  pages = 223–231 |
  date = 1978}}</ref>

The [[reachability problem]] for Petri nets was known to be {{Sans-serif|EXPSPACE}}-hard for a long time,<ref>{{cite journal | last = Lipton | first = R. | url = http://citeseer.ist.psu.edu/contextsummary/115623/0 | title = The Reachability Problem Requires Exponential Space | journal = Technical Report 62 | publisher = Yale University | date = 1976 }}</ref> but shown to be [[Nonelementary problem|nonelementary]],<ref>{{cite conference | author = Wojciech Czerwiński Sławomir Lasota Ranko S Lazić Jérôme Leroux Filip Mazowiecki
| title = The reachability problem for Petri nets is not elementary | book-title = STOC 19 | date = 2019}}</ref> so probably not in {{Sans-serif|EXPSPACE}}. In 2022 it was shown to be [[Ackermann function|Ackermann]]-complete.<ref name=":1">{{Cite book |last=Leroux |first=Jerome |chapter=The Reachability Problem for Petri Nets is Not Primitive Recursive |date=February 2022 |title=2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS) |chapter-url=https://ieeexplore.ieee.org/document/9719763 |publisher=IEEE |pages=1241–1252 |doi=10.1109/FOCS52979.2021.00121 |isbn=978-1-6654-2055-6|arxiv=2104.12695 }}</ref><ref name=":0">{{Cite web |last=Brubaker |first=Ben |date=4 December 2023 |title=An Easy-Sounding Problem Yields Numbers Too Big for Our Universe |url=https://www.quantamagazine.org/an-easy-sounding-problem-yields-numbers-too-big-for-our-universe-20231204/ |website=[[Quanta Magazine]]}}</ref>