Computation theory and logic
Verification of sequential and concurrent programs
Verification of sequential and concurrent programs
Sequential abstract-state machines capture sequential algorithms
ACM Transactions on Computational Logic (TOCL)
Ten Years of Hoare's Logic: A Survey—Part I
ACM Transactions on Programming Languages and Systems (TOPLAS)
An axiomatic basis for computer programming
Communications of the ACM
Multi-dimensional rankings, program termination, and complexity bounds of flowchart programs
SAS'10 Proceedings of the 17th international conference on Static analysis
Yuri, logic, and computer science
Fields of logic and computation
Optimizing database-backed applications with query synthesis
Proceedings of the 34th ACM SIGPLAN conference on Programming language design and implementation
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Hoare logic is a widely recommended verification tool. There is, however, a problem of finding easily checkable loop invariants; it is known that decidable assertions do not suffice to verify while programs, even when the pre- and postconditions are decidable. We show here a stronger result: decidable invariants do not suffice to verify single-loop programs. We also show that this problem arises even in extremely simple contexts. Let N be the structure consisting of the set of natural numbers together with the functions S(x)=x+1,D(x)=2(x)=***x/2***. There is a single-loop program *** using only three variables x,y,z such that the asserted program x=y=z=0 *** false is partially correct on N but any loop invariant I(x,y,z) for this asserted program is undecidable.