List of PSPACE-complete problems

Here are some of the more commonly known problems that are PSPACE-complete when expressed as decision problems. This list is in no way comprehensive.

Games and puzzles
Generalized versions of:


 * Amazons
 * Atomix
 * Checkers if a draw is forced after a polynomial number of non-jump moves
 * Dyson Telescope Game
 * Cross Purposes
 * Geography
 * Two-player game version of Instant Insanity
 * Ko-free Go
 * Ladder capturing in Go
 * Gomoku
 * Hex
 * Konane
 * Lemmings
 * Node Kayles
 * Poset Game
 * Reversi
 * River Crossing
 * Rush Hour
 * Finding optimal play in Mahjong solitaire
 * Scrabble
 * Sokoban
 * Super Mario Bros.
 * Black Pebble game
 * Black-White Pebble game
 * Acyclic pebble game
 * One-player pebble game
 * Token on acyclic directed graph games:

Logic

 * Quantified boolean formulas


 * First-order logic of equality
 * Provability in intuitionistic propositional logic
 * Satisfaction in modal logic S4
 * First-order theory of the natural numbers under the successor operation
 * First-order theory of the natural numbers under the standard order
 * First-order theory of the integers under the standard order
 * First-order theory of well-ordered sets
 * First-order theory of binary strings under lexicographic ordering
 * First-order theory of a finite Boolean algebra
 * Stochastic satisfiability
 * Linear temporal logic satisfiability and model checking

Lambda calculus
Type inhabitation problem for simply typed lambda calculus

Circuit theory
Integer circuit evaluation

Automata theory

 * Word problem for linear bounded automata
 * Word problem for quasi-realtime automata
 * Emptiness problem for a nondeterministic two-way finite state automaton
 * Equivalence problem for nondeterministic finite automata
 * Word problem and emptiness problem for non-erasing stack automata
 * Emptiness of intersection of an unbounded number of deterministic finite automata


 * A generalized version of Langton's Ant
 * Minimizing nondeterministic finite automata

Formal languages

 * Word problem for context-sensitive language
 * Intersection emptiness for an unbounded number of regular languages
 * Regular Expression Star-Freeness
 * Equivalence problem for regular expressions
 * Emptiness problem for regular expressions with intersection.
 * Equivalence problem for star-free regular expressions with squaring.
 * Covering for linear grammars
 * Structural equivalence for linear grammars
 * Equivalence problem for Regular grammars
 * Emptiness problem for ET0L grammars
 * Word problem for ET0L grammars
 * Tree transducer language membership problem for top down finite-state tree transducers

Graph theory

 * succinct versions of many graph problems, with graphs represented as Boolean circuits, ordered binary decision diagrams or other related representations:
 * s-t reachability problem for succinct graphs. This is essentially the same as the simplest plan existence problem in automated planning and scheduling.
 * planarity of succinct graphs
 * acyclicity of succinct graphs
 * connectedness of succinct graphs
 * existence of Eulerian paths in a succinct graph
 * Bounded two-player Constraint Logic
 * Canadian traveller problem.
 * Determining whether routes selected by the Border Gateway Protocol will eventually converge to a stable state for a given set of path preferences
 * Deterministic constraint logic (unbounded)
 * Dynamic graph reliability.
 * Graph coloring game
 * Node Kayles game and clique-forming game: two players alternately select vertices and the induced subgraph must be an independent set (resp. clique). The last to play wins.
 * Nondeterministic Constraint Logic (unbounded)

Others

 * Finite horizon POMDPs (Partially Observable Markov Decision Processes).
 * Hidden Model MDPs (hmMDPs).
 * Dynamic Markov process.
 * Detection of inclusion dependencies in a relational database
 * Computation of any Nash equilibrium of a 2-player normal-form game, that may be obtained via the Lemke–Howson algorithm.
 * The Corridor Tiling Problem: given a set of Wang tiles, a chosen tile $$T_0$$ and a width $$n$$ given in unary notation, is there any height $$m$$ such that an $$n\times m$$ rectangle can be tiled such that all the border tiles are $$T_0$$?