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
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
Automata and language theory
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 and a width given in unary notation, is there any height such that an rectangle can be tiled such that all the border tiles are ?
See also
List of NP-complete problems
Notes
References
Eppstein's page on computational complexity of games
The Complexity of Approximating PSPACE-complete problems for hierarchical specifications