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Undecidable decision problem introduced by Emil Post
The Post correspondence problem is an undecidable decision problem that was introduced by Emil Post in 1946. Because it is simpler than the halting problem
Post_correspondence_problem
American mathematician and logician (1897 – 1954)
all. Correspondence systems were introduced by Post in 1946 to give simple examples of undecidability. He showed that the Post correspondence problem (PCP)
Emil_Leon_Post
Generalization of the pumping lemma for context-free languages
Ogden's paper) Construction Given any Post correspondence problem over binary strings, we reduce it to a decision problem over a CFG. Given any two lists of
Ogden's_lemma
of the Post correspondence problem Shortest common supersequence over multiple sequences Extension of the string-to-string correction problem Bag (Corral)
List_of_NP-complete_problems
Type of grammar for describing formal languages
reason for this is that any instance of the Post correspondence problem reduces to an instance of the problem of deciding whether a parsing expression language
Parsing_expression_grammar
The halting problem is not in ExpGenP for any model of Turing machine, The Post correspondence problem is in ExpGenP. The decision problem for Presburger
Generic-case_complexity
Computational problems no algorithm can solve
Determining whether a λ-calculus formula has a normal form. The Post correspondence problem: whether a tag system halts. There are many variants thereof
List_of_undecidable_problems
Rule system for formal languages
undecidability of this problem follows from the fact that if an algorithm to determine ambiguity existed, the Post correspondence problem could be decided,
Context-free_grammar
Computing using molecular biology hardware
— Describes a solution for the bounded Post correspondence problem, a hard-on-average NP-complete problem. Also available here: [1] Baum, E. B. (1995-04-28)
DNA_computing
Topics referred to by the same term
explicit port forwarding rules on default gateways Post correspondence problem, an important problem in computability theory Primary Control Program, an
PCP
Branch of mathematical linguistics
{\displaystyle x} in the group. Many word problems are undecidable based on the Post correspondence problem. Any two homomorphisms g , h {\displaystyle
Combinatorics_on_words
Type of a context-free grammar
necessary to find a regular partition for G, can be reduced to the Post correspondence problem. Every LLR grammar is LR-regular (LRR, the corresponding[clarification
LL_grammar
Formal language
hand, the problem is undecidable. Some other recursively enumerable languages that are not recursive include: Post correspondence problem Mortality (computability
Recursively enumerable language
Recursively_enumerable_language
Mario Tokoro, ed. (2010). "9". e: From Understanding Principles to Solving Problems. IOS Press. pp. 223–224. ISBN 978-1-60750-468-9. Cristopher Moore; Stephan
List of pioneers in computer science
List_of_pioneers_in_computer_science
Type of context-free grammar
problem of whether an arbitrary grammar is ambiguous is undecidable because it can be shown that it is equivalent to the Post correspondence problem.
Ambiguous_grammar
Overview of and topical guide to logic
Church–Turing thesis Lambda calculus List of undecidable problems Post correspondence problem Post's theorem Primitive recursive function Recursion (computer
Outline_of_logic
String rewriting system
for Turing machines to an instance of the word problem (see Post correspondence problem). Concretely, Post devised an encoding as a finite string of the
Semi-Thue_system
Graph rewriting framework
Termination for DPO graph rewriting is undecidable because the Post correspondence problem can be reduced to it. DPO graph rewriting can be viewed as a
Double pushout graph rewriting
Double_pushout_graph_rewriting
Entscheidungsproblem Halting problem Correctness Post correspondence problem Decidable language Undecidable language Word problem for groups Wang tile Penrose
List of computability and complexity topics
List_of_computability_and_complexity_topics
Complexity class
grammars have RE-complete membership problems.) The validity problem for first-order logic. Post correspondence problem: Given a list of pairs of strings
RE_(complexity)
Category of mathematical proof
of an example, that not every problem of this class is solvable" (Undecidable p. 90)) 1946: Post correspondence problem (cf Hopcroft and Ullman p. 193ff
Proof_of_impossibility
American sci-fi television series
3 Body Problem is an American science fiction television series created by David Benioff, D. B. Weiss, and Alexander Woo. It is the third adaptation of
3_Body_Problem_(TV_series)
Church–Rosser theorem Calculus of constructions Combinatory logic Post correspondence problem Kleene's recursion theorem Recursively enumerable set Recursively
List of mathematical logic topics
List_of_mathematical_logic_topics
French computer scientist
Autebert. With Yuri Matiyasevich he obtained results about the Post correspondence problem. He won the 2002 Gödel Prize "for proving that equivalence of
Géraud_Sénizergues
Conformity to reality
have been proposed, but its precise definition remains contested. The correspondence theory holds that a statement is true if it corresponds to facts. According
Truth
Visual sensation of spatial awareness
neural models for binocular depth vision and for the solution of the correspondence problem to be discussed. These cells are part of two neurophysiological
Stereopsis
Game of chess via postal system or e-mail
weeks, or months; a game played by post between players in different countries might last several years. Correspondence chess differs from over-the-board
Correspondence_chess
following is a list of notable unsolved problems grouped into broad areas of physics. Some of the major unsolved problems in physics are theoretical, meaning
List of unsolved problems in physics
List_of_unsolved_problems_in_physics
Philosophical question
and the Problem of Animal Suffering. Oxford University Press. p. 2. ISBN 978-0-19-155327-1., cites letter to J. D. Hooker (Darwin Correspondence Project
Problem_of_evil
uniquely decodable by definition. Timeline of information theory Post's correspondence problem is similar, yet undecidable. Sardinas & Patterson (1953). Knuth
Sardinas–Patterson_algorithm
Ongoing UK legal and political scandal
subpostmasters had reported problems with the new software, and Fujitsu was aware that Horizon contained software bugs as early as 1999, the Post Office insisted
British_Post_Office_scandal
Physics principle formulated by Niels Bohr
In physics, a correspondence principle is any one of several premises or assertions about the relationship between classical and quantum mechanics. The
Correspondence_principle
18th-century American political organizations
The committees of correspondence were a collection of American political organizations that sought to coordinate opposition to the British Parliament and
Committees_of_correspondence
Concept involving online bot activity
"feel like they were created for search engines instead of people". In correspondence with Gizmodo, a Google spokesperson acknowledged the role of generative
Dead_Internet_theory
Concept regarding objective facts
research and public debate about post-truth assumes a particular theory of truth, what philosophers call a correspondence theory of truth. The latter might
Post-truth
System for transporting documents and other small packages
accessibility of email. Online post offices have emerged to give recipients a means of receiving traditional correspondence mail in a scanned electronic
American conservative newspaper
stated that the "New York Post is no longer merely a journalistic problem. It is a social problem—a force for evil." The Post has been accused of contorting
New_York_Post
Compact astronomical body
Hubble Space Telescope. Unsolved problem in physics Is physical information lost in black holes? More unsolved problems in physics According to the no-hair
Black_hole
Measure of unsolvability
sequence ai of degrees such that a′i+1 ≤ ai for each i. Post's theorem establishes a close correspondence between the arithmetical hierarchy and finitely iterated
Turing_degree
Impossible task in computing
mathematics and computer science, the Entscheidungsproblem (German for 'decision problem'; pronounced [ɛntˈʃaɪ̯dʊŋspʁoˌbleːm]) is a challenge posed by David Hilbert
Entscheidungsproblem
Dordrecht. He engaged in philosophical correspondence with Baruch Spinoza regarding the problem of evil. Their correspondence consisted of four letters each,
Willem_van_Blijenbergh
Mathematician
notions of elliptic module and the theory of the geometric Langlands correspondence. Drinfeld introduced the notion of a quantum group (independently discovered
Vladimir_Drinfeld
Optimization technique
variety of low-level computer vision problems (early vision), such as image smoothing, the stereo correspondence problem, image segmentation, object co-segmentation
Graph cuts in computer vision and artificial intelligence
Graph_cuts_in_computer_vision_and_artificial_intelligence
Logical connective AND
also used in SQL operations to form database queries. The Curry–Howard correspondence relates logical conjunction to product types. The membership of an element
Logical_conjunction
Mathematician (1845–1918)
theory in mathematics. Cantor established the importance of one-to-one correspondence between the members of two sets, defined infinite and well-ordered sets
Georg_Cantor
Awards for journalism and related fields
Official website "The Pulitzer Prizes". The New York Times. "Washington Post and Los Angeles Times Each Win Three Pulitzer Prizes". The New York Times
2003_Pulitzer_Prize
Country in West Asia
requested that foreign delegates begin using the endonym "Iran" in formal correspondence. Subsequently, "Iran" and "Iranian" were standardised as the terms referring
Iran
Awards for journalism and related fields
Reporting and Commentary Criticism Former Editorial Writing Reporting Correspondence Photography Commentary Letters, Drama, and Music Biography Drama Fiction
1988_Pulitzer_Prize
Files on Jeffrey Epstein and his affiliates
estate. These releases included portions of Epstein's contact records, correspondence, and photographs. FBI Director Kash Patel testified before the Senate
Epstein_files
Political party in the United States
Memory. JHU Press. ISBN 978-1-4214-2303-6. Jackson, Andrew (1928). Correspondence of Andrew Jackson: 1833-1838. Carnegie institution of Washington. p
Democratic Party (United States)
Democratic_Party_(United_States)
Philosophical question of how to distinguish between science and non-science
Lakatos-Feyerabend Correspondence. University of Chicago Press. p. 20. ISBN 9780226467740. LCCN 99013581. The demarcation problem may be formulated in
Demarcation_problem
American domestic terrorist (1942–2023)
Reprint and solutions to "Problem 787" (above) Kaczynski, Theodore (1995). "Industrial Society and Its Future". The Washington Post. Archived from the original
Ted_Kaczynski
Archived from the original on 8 October 2019. Retrieved 30 October 2019. "Correspondence with Chloe Smith MP" (PDF). Parliament of the United Kingdom. Archived
2024 United Kingdom general election
2024_United_Kingdom_general_election
Literary genre
science fiction fanzine, The Comet, was published in 1930 by the Science Correspondence Club in Chicago, Illinois. As of 2025, one of the best known fanzines
Science_fiction
Honorific for women who are married
March 2023. Retrieved 11 March 2023. "Guide to Addressing Correspondence". The Emily Post Institute, Inc. Archived from the original on 2016-07-03. Retrieved
Mrs.
People in files on Jeffrey Epstein
action. David Blaine is an American magician. Files showed a years-long correspondence with Epstein and regular dinners between 2012 and 2016. In 2015, Blaine
List of people named in the Epstein files
List_of_people_named_in_the_Epstein_files
Independent agency of the U.S. federal government
receive free post office boxes if the USPS declines to provide door-to-door delivery to their location or a nearby box. People with medical problems can request
United_States_Postal_Service
Soviet mathematician (1903–1979)
would imply a solution to Turing's halting problem. Embedding implies failure to create a correspondence between algorithms and indexing (naturally uncountably
Andrey_Markov_Jr.
Mathematics award
Sylvia; Gruber, David (21 August 2006). "Manifold Destiny: A legendary problem and the battle over who solved it". The New Yorker. Archived from the original
Fields_Medal
Swiss mathematician (1707–1783)
greatest mathematician of the 18th century. His 866 publications and his correspondence were collected in the Opera Omnia Leonhard Euler. Several great mathematicians
Leonhard_Euler
Burgum's wife Kathryn heard and seen in Forbes's live coverage. In correspondence with Snopes, White House spokesman Steven Cheung denied the rumor that
Age and health concerns about Donald Trump
Age_and_health_concerns_about_Donald_Trump
Class of algorithms
last subtree. Visit the current node for post-order traversal. Depending on the problem at hand, pre-order, post-order, and especially one of the number
Tree_traversal
writing but received no response, and added that FIFA later treated its correspondence as an appeal without providing a formal decision or explanation. European
List of 2026 FIFA World Cup controversies
List_of_2026_FIFA_World_Cup_controversies
Chess composition whose solution is a mate or other clear objective
honour a problem has received when it is republished. Solving tournaments also fall into two main types. In tourneys conducted by correspondence, the participants
Chess_problem
Type of correspondence consisting of a letter and money
a single envelope. This differentiates a qiaopi from other forms of correspondence such as mail. Qiaopi is sometimes referred to as zhengpi ("main pi")
Qiaopi
obtainable or possibly even extant (e.g. old newspaper articles, personal correspondence, and television broadcasts) but nonetheless mentioned in more readily
List of giant squid specimens and sightings
List_of_giant_squid_specimens_and_sightings
Mayor of New York City
George's Grammar School in Mowbray from 1996 to 1998, during the early post-apartheid years. He later said that the experience of living in Cape Town
Zohran_Mamdani
Government system where political power lies with the people
Vanberg, Georg S. (2000). "Election Laws, Disproportionality and Median Correspondence: Implications for Two Visions of Democracy". British Journal of Political
Democracy
Anonymous reverser
Internet. While his identity is unknown, reverse engineer Fravia had email correspondence with him and spread his tutorials. Old Red Cracker founded the so-called
Old_Red_Cracker
Country in Northern Europe
Polish–Lithuanian Commonwealth in 1795. Internal state acts, international correspondence and resolutions of the Sejm of the Polish–Lithuanian Commonwealth had
Lithuania
Mathematical classification
classifications) is a situation where certain kinds of objects are in correspondence with simply laced Dynkin diagrams. The question of giving a common origin
ADE_classification
Cohort born from 2010s to 2020s
historical records and documents of the United States, such as the correspondence of Abraham Lincoln, were written by hand in cursive, and students today
Generation_Alpha
Math theorem about sphere packing
He had started to study arrangements of spheres as a result of his correspondence with the English mathematician and astronomer Thomas Harriot in 1606
Kepler_conjecture
Deaths involving use of large language models
a Belgian man in his thirties died by suicide following a six-week correspondence with a chatbot named Eliza on the application Chai. According to his
Deaths_linked_to_chatbots
British Army officer, diplomat and writer (1888–1935)
Lucas More Correspondence with Writers Correspondence with Edward and David Garnett Correspondence with Henry Williamson Correspondence with the Political
T._E._Lawrence
American writer (1933–2023)
inspiration. After 1958, McCarthy wrote all of his literary work and correspondence with a mechanical typewriter. He originally used a Royal but went looking
Cormac_McCarthy
Ongoing genocide in the Gaza Strip
in Investigating and Prosecuting Charges of Genocide in Romania". Problems of Post-Communism. 72 (1): 97–111. Grim, Ryan (2 March 2024). "WCNSF: The Most
Gaza_genocide
Awards for journalism and related fields
aerospace industry, notably an exhaustive investigation of rudder control problems on the Boeing 737, which contributed to new FAA requirements for major
1997_Pulitzer_Prize
Northwest Semitic language
but also poetry, philosophy, science and medicine, commerce, daily correspondence and contracts. There have been many deviations from this generalization
Hebrew_language
Iron Age culture in central Italy
Latial burial practices. Sestieri and De Santis suggest that these correspondences provide further attestation of contact between Latium and southern
Latial_culture
Mental phenomenon of holding contradictory beliefs
function in the reality of society, human beings continually adjust the correspondence of their mental attitudes and personal actions; such continual adjustments
Cognitive_dissonance
Archaeological method of relative dating
for contextual and frequency problems is based on correspondence analysis. The sequence of the first axis of a correspondence analysis is considered the
Seriation_(archaeology)
Russian-American mathematician
general framework for the analytic Langlands correspondence, 2023. Frenkel, Edward (October 2012). "The Fifth problem: math & anti-Semitism in the Soviet Union"
Edward_Frenkel
William George Jordan self-help book
a long-running correspondence with William George Jordan. Jordan, William George (2017-11-21). The Power of Truth: Individual Problems and Possibilities
The_Power_of_Truth
American anthropologist (1942–1995)
work on the island of Java and blacksmithing in Indonesia. To address the problem of poverty in rural villages, she designed microcredit programs while working
Ann_Dunham
Period of British history after World War II and during the Cold War
7.3 (2005): 79–123. Peter G. Boyle (1990). The Churchill-Eisenhower Correspondence, 1953–1955. U North Carolina Press. pp. 52–54. ISBN 9780807849514. Archived
Post-war_Britain_(1945–1979)
Armed conflict in South Asia
Pakistan Problem". The New York Times. Retrieved 18 May 2025. "India-Pakistan ceasefire holds. But the battle lines have changed". The Washington Post. 12
2025_India–Pakistan_conflict
American political party
the Department of State sympathetic to the party, the confidential correspondence, concerning political and economic matters in Europe, ended up in the
Communist_Party_USA
Conventions for text-based Internet fora
shows the latest replies. This appears to be advantageous for business correspondence, where an e-mail thread can dupe others into believing it is an "official"
Posting_style
1995 manifesto by Ted Kaczynski
he continued to clarify his philosophy with other writers through correspondence, and by composing two books which were published during his incarceration
Industrial Society and Its Future
Industrial_Society_and_Its_Future
Mode of delivering education to students who are not physically present
with others, and retain self-discipline. Historically, it involved correspondence courses wherein the student corresponded with the school via mail, but
Distance_education
Businessman and public official (born 1971)
invited Musk to visit his private island on multiple occasions. The correspondence showed that while Epstein repeatedly encouraged Musk to attend, Musk
Elon_Musk
American murderer (born 1958)
McNair's escape and his time as a fugitive is through McNair's prison correspondence with a Canadian journalist, Byron Christopher. McNair had previously
Richard_Lee_McNair
Human disease
from Latin: scabere, lit. 'to scratch'. It is a particular public health problem in crowded settings such as care homes, schools, refugee camps, prisons
Scabies
Network service attack performed by multiple fake identities
remote entity can be aware of identities without necessarily knowing the correspondence of identities to local entities. By default, each distinct identity
Sybil_attack
Supreme Leader of Iran since 2026
theocratic establishment. On 6 April, The Times reported diplomatic correspondence based on US and Israeli intelligence asserting that Khamenei is unconscious
Mojtaba_Khamenei
Congolese politician and independence leader (1925–1961)
his immediate assistants, set up the schedule for the day, went over correspondence, which he answered. Without a stop until evening he was receiving salesmen
Patrice_Lumumba
Family of physicist Albert Einstein
the first child of Mileva Marić and Albert Einstein. According to the correspondence between her parents, Lieserl was born on 27 January 1902, a year before
Einstein_family
Changes introduced to the Soviet Union time system
the introduction of summer time, it was necessary to establish the correspondence of the applied time to the administrative time zones, that is, to restore
Decree_time
List of subspecies of the common pheasant
Herals of the Game Management. 15 (3). FGBU VO "Russian State Agragrian Correspondence University: 166–175. Retrieved 2026-01-25. Erikhov, S. N.; Gistsov,
Subspecies of Phasianus colchicus
Subspecies_of_Phasianus_colchicus
POST CORRESPONDENCE-PROBLEM
POST CORRESPONDENCE-PROBLEM
Female
English
 English name derived from the flower name which originally meant "a line of verse engraved on the inner surface of a ring," but later acquired the POSY means "bouquet, flower." Pet form of English Josephine, meaning "(God) shall add (another son)."Â
Surname or Lastname
English
English : from Middle English port ‘gateway’, ‘entrance’ (Old French porte, from Latin porta), hence a topographic name for someone who lived near the gates of a fortified town or city, typically, the man in charge of them. Compare Porter 1.English : topographic name for someone who lived near a harbor or in a market town, from the homonymous Middle English port (Old English port ‘harbor’, ‘market town’, from Latin portus ‘harbor’, ‘haven’, reinforced in Middle English by Old French port, from the same source).German : topographic name for someone who lived near a (city) gate, from Middle Low German porte (modern German Pforte) (see sense 1).Jewish (from Lithuania and Belarus) : unexplained.
Surname or Lastname
English, Scottish, French, and Catalan
English, Scottish, French, and Catalan : topographic name for
someone who lived near a bridge, Middle English, Old French, Catalan
pont (Latin pons, genitive pontis).Catalan : habitational name from any of the numerous places named
with Pont.Dutch : variant of
Pond 2.A Pont from the Lorraine region of France is documented in Quebec City in
1640; Pont appears to be a secondary surname to
Male
Hebrew
(×ַגְרï‹×Ÿ) Hebrew name AGRON means "correspondence" or "vocabulary."
Boy/Male
Hebrew Spanish
May Jehovah add/give increase.
Boy/Male
Australian, Danish, German, Hebrew, Latin, Swedish
May Jehovah Give Increase; Experienced in Battle
Male
Swiss
, sportive.
Boy/Male
Arabic, Muslim
Friend of the Prophet Muhammad
Boy/Male
Muslim
Friend
Surname or Lastname
English (now most common in northern Ireland)
English (now most common in northern Ireland) : probably a habitational name from a lost or unidentified place, most likely somewhere in Lancashire or Yorkshire.
Male
Dutch
, just.
Boy/Male
Indian
Pillar, Post, Support
Boy/Male
Arabic, Muslim, Parsi
Friend; Sweetheart
Surname or Lastname
English
English : occupational name for an innkeeper, from Middle English, Old French (h)oste ‘host’, ‘guest’.Danish (Høst) : nickname from høst ‘harvest’, ‘autumn’ (see Herbst).French : from Old French ost ‘army’, hence an occupational name for a soldier.Dutch : from the Germanic personal name Austa, meaning ‘east’.German : habitational name from either of two places called Host, near Koblenz and near Bitburg.
Boy/Male
Hindu
Month in Hindu calendar
Boy/Male
Hindu, Indian
Month in Hindu Calender
Boy/Male
Indian
Friend
Boy/Male
Indian
Pillar, Post, Support
Girl/Female
British, Christian, English
Small Flower
Surname or Lastname
English
English : from a medieval personal name, a short form of Philpott.English : topographic name for someone who lived by a depression in the ground, from Middle English pot ‘drinking or storage vessel’ used in this transferred sense, or a habitational name from one of the minor places deriving their name from this word, in the sense ‘pit’, ‘hole’.English and North German (Lower Rhine-Westphalia) : metonymic occupational name for a potter, from Middle English, Middle Low German pot ‘pot’. See also Potter.North German : topographic name for someone living on a low-lying plot, from Low German dialect pÅt ‘puddle’.
POST CORRESPONDENCE-PROBLEM
POST CORRESPONDENCE-PROBLEM
Girl/Female
Tamil
Anwika | அநà¯à®µà®¿à®•à®¾
Boy/Male
Hindu, Indian, Telugu
Name of Vishnu
Male
Italian
 Italian, Portuguese and Spanish form of Latin Demetrius, DEMETRIO means "loves the earth" or "follower of Demeter."
Female
English
English pet form of Latin Anna, ANNIE means "favor; grace."
Boy/Male
Tamil
Garden
Boy/Male
Arabic
Pure Silver
Boy/Male
American, Arabic, Muslim, Pakistani
A Person who Always Help; Helper
Girl/Female
Hindu
Daughter
Surname or Lastname
English
English : habitational name from a place in Gloucestershire named Bledisloe, from the Old English personal name Blīð (a byname meaning ‘cheerful’) + Old English hlÄw ‘mound’, ‘tumulus’.
Biblical
hopes of life
POST CORRESPONDENCE-PROBLEM
POST CORRESPONDENCE-PROBLEM
POST CORRESPONDENCE-PROBLEM
POST CORRESPONDENCE-PROBLEM
POST CORRESPONDENCE-PROBLEM
adv.
With post horses; hence, in haste; as, to travel post.
v. t.
Ruined or destroyed, either physically or morally; past help or hope; as, a ship lost at sea; a woman lost to virtue; a lost soul.
n.
The letters which pass between correspondents.
n.
One of two suspending posts in a roof truss, or other framed truss of similar form. See King-post.
v. t.
To carry, as an account, from the journal to the ledger; as, to post an account; to transfer, as accounts, to the ledger.
n.
Same as Correspondence, 3.
n.
A station, office, or position of service, trust, or emolument; as, the post of duty; the post of danger.
n.
A post-temporal bone.
n.
See under 4th Post.
pl.
of Correspondency
imp. & p. p.
of Cost
v. t.
To hold up to public blame or reproach; to advertise opprobriously; to denounce by public proclamation; as, to post one for cowardice.
v. i.
To travel with post horses; figuratively, to travel in haste.
v. t.
To attach to a post, a wall, or other usual place of affixing public notices; to placard; as, to post a notice; to post playbills.
n.
A piece of timber, metal, or other solid substance, fixed, or to be fixed, firmly in an upright position, especially when intended as a stay or support to something else; a pillar; as, a hitching post; a fence post; the posts of a house.
v. t.
To assign to a station; to set; to place; as, to post a sentinel.
a.
After death; as, post-mortem rigidity.
v. t.
To place in the care of the post; to mail; as, to post a letter.
n.
Same as King-post.