## Viktor Kuncak and Martin Rinard.
Typestate checking and regular graph constraints.
Technical Report 863, MIT LCS, 2002.

We introduce regular graph constraints and explore their
decidability properties. The motivation for regular graph
constraints is 1) type checking of changing types of objects
in the presence of linked data structures, 2) shape analysis
techniques, and 3) generalization of similar constraints
over trees and grids. We define a subclass of graphs called
heaps as an abstraction of the data structures that a
program constructs during its execution. We prove that
determining the validity of implication for regular graph
constraints over the class of heaps is undecidable. We show
undecidability by exhibiting a characterization of certain
"corresponder graphs" in terms of presence and absence of
homomorphisms to a finite number of fixed graphs. The
undecidability of implication of regular graph constraints
implies that there is no algorithm that will verify that
procedure preconditions are met or that the invariants are
maintained when these properties are expressed in any
specification language at least as expressive as regular
graph constraints.

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