59,568 research outputs found
Second-Order Functions and Theorems in ACL2
SOFT ('Second-Order Functions and Theorems') is a tool to mimic second-order
functions and theorems in the first-order logic of ACL2. Second-order functions
are mimicked by first-order functions that reference explicitly designated
uninterpreted functions that mimic function variables. First-order theorems
over these second-order functions mimic second-order theorems universally
quantified over function variables. Instances of second-order functions and
theorems are systematically generated by replacing function variables with
functions. SOFT can be used to carry out program refinement inside ACL2, by
constructing a sequence of increasingly stronger second-order predicates over
one or more target functions: the sequence starts with a predicate that
specifies requirements for the target functions, and ends with a predicate that
provides executable definitions for the target functions.Comment: In Proceedings ACL2 2015, arXiv:1509.0552
Classical Verification of Quantum Computations
We present the first protocol allowing a classical computer to interactively
verify the result of an efficient quantum computation. We achieve this by
constructing a measurement protocol, which enables a classical verifier to use
a quantum prover as a trusted measurement device. The protocol forces the
prover to behave as follows: the prover must construct an n qubit state of his
choice, measure each qubit in the Hadamard or standard basis as directed by the
verifier, and report the measurement results to the verifier. The soundness of
this protocol is enforced based on the assumption that the learning with errors
problem is computationally intractable for efficient quantum machines
Algebras of multiplace functions for signatures containing antidomain
We define antidomain operations for algebras of multiplace partial functions.
For all signatures containing composition, the antidomain operations and any
subset of intersection, preferential union and fixset, we give finite
equational or quasiequational axiomatisations for the representation class. We
do the same for the question of representability by injective multiplace
partial functions. For all our representation theorems, it is an immediate
corollary of our proof that the finite representation property holds for the
representation class. We show that for a large set of signatures, the
representation classes have equational theories that are coNP-complete.Comment: 33 pages. Added brief discussion of square algebra
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