List of PSPACE-complete problems
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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[1]
- Atomix[2]
- Checkers if a draw is forced after a polynomial number of non-jump moves[3]
- Dyson Telescope Game[4]
- Cross Purposes[5]
- Geography
- Two-player game version of Instant Insanity
- Ko-free Go[6]
- Ladder capturing in Go[7]
- Gomoku[8]
- Hex[9]
- Konane[5]
- Lemmings[10]
- Node Kayles[11]
- Poset Game[12]
- Reversi[13]
- River Crossing[14]
- Rush Hour[14]
- Finding optimal play in Mahjong solitaire[15]
- Scrabble[16]
- Sokoban[14]
- Super Mario Bros.[17]
- Black Pebble game[18]
- Black-White Pebble game[19]
- Acyclic pebble game[20]
- One-player pebble game[20]
- Token on acyclic directed graph games:[11]
Logic
- Quantified boolean formulas
- First-order logic of equality[21]
- Provability in intuitionistic propositional logic
- Satisfaction in modal logic S4[21]
- First-order theory of the natural numbers under the successor operation[21]
- First-order theory of the natural numbers under the standard order[21]
- First-order theory of the integers under the standard order[21]
- First-order theory of well-ordered sets[21]
- First-order theory of binary strings under lexicographic ordering[21]
- First-order theory of a finite Boolean algebra[21]
- Stochastic satisfiability[22]
- Linear temporal logic satisfiability and model checking[23]
Lambda calculus
Type inhabitation problem for simply typed lambda calculus
Automata and language theory
Summarize
Perspective
Circuit theory
Integer circuit evaluation[24]
Automata theory
- Word problem for linear bounded automata[25]
- Word problem for quasi-realtime automata[26]
- Emptiness problem for a nondeterministic two-way finite state automaton[27][28]
- Equivalence problem for nondeterministic finite automata[29][30]
- Word problem and emptiness problem for non-erasing stack automata[31]
- Emptiness of intersection of an unbounded number of deterministic finite automata[32]
- A generalized version of Langton's Ant[33]
- Minimizing nondeterministic finite automata[34]
Formal languages
- Word problem for context-sensitive language[35]
- Intersection emptiness for an unbounded number of regular languages [32]
- Regular Expression Star-Freeness [36]
- Equivalence problem for regular expressions[21]
- Emptiness problem for regular expressions with intersection.[21]
- Equivalence problem for star-free regular expressions with squaring.[21]
- Covering for linear grammars[37]
- Structural equivalence for linear grammars[38]
- Equivalence problem for Regular grammars[39]
- Emptiness problem for ET0L grammars[40]
- Word problem for ET0L grammars[41]
- Tree transducer language membership problem for top down finite-state tree transducers[42]
Graph theory
- succinct versions of many graph problems, with graphs represented as Boolean circuits,[43] ordered binary decision diagrams[44] 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[11]
- Canadian traveller problem.[45]
- Determining whether routes selected by the Border Gateway Protocol will eventually converge to a stable state for a given set of path preferences[46]
- Deterministic constraint logic (unbounded)[47]
- Dynamic graph reliability.[22]
- Graph coloring game[48]
- Node Kayles game and clique-forming game:[49] 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)[11]
Others
- Finite horizon POMDPs (Partially Observable Markov Decision Processes).[50]
- Hidden Model MDPs (hmMDPs).[51]
- Dynamic Markov process.[22]
- Detection of inclusion dependencies in a relational database[52]
- Computation of any Nash equilibrium of a 2-player normal-form game, that may be obtained via the Lemke–Howson algorithm.[53]
- 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 ?[54][55]
See also
Notes
References
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