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We introduce a family of local models of dynamics based on ``word problems''from computer science and group theory, for which we can place rigorous lowerbounds on relaxation timescales. These models can be regarded either as randomcircuit or local Hamiltonian dynamics, and include many familiar examples ofconstrained dynamics as special cases. The configuration space of these modelssplits into dynamically disconnected sectors, and for initial states to relax,they must ``work out'' the other states in the sector to which they belong.When this problem has a high time complexity, relaxation is slow. In some ofthe cases we study, this problem also has high space complexity. When the spacecomplexity is larger than the system size, an unconventional type of jammingtransition can occur, whereby a system of a fixed size is not ergodic, but canbe made ergodic by appending a large reservoir of sites in a trivial productstate. This manifests itself in a new type of Hilbert space fragmentation thatwe call fragile fragmentation. We present explicit examples where slowrelaxation and jamming strongly modify the hydrodynamics of conserveddensities. In one example, density modulations of wavevector $q$ exhibit almostno relaxation until times $O(\exp(1/q))$, at which point they abruptlycollapse. We also comment on extensions of our results to higher dimensions.

Glassy word problems: ultraslow relaxation, Hilbert space jamming, and computational complexity