13 research outputs found
Towards Verifying Nonlinear Integer Arithmetic
We eliminate a key roadblock to efficient verification of nonlinear integer
arithmetic using CDCL SAT solvers, by showing how to construct short resolution
proofs for many properties of the most widely used multiplier circuits. Such
short proofs were conjectured not to exist. More precisely, we give n^{O(1)}
size regular resolution proofs for arbitrary degree 2 identities on array,
diagonal, and Booth multipliers and quasipolynomial- n^{O(\log n)} size proofs
for these identities on Wallace tree multipliers.Comment: Expanded and simplified with improved result
Multitask Efficiencies in the Decision Tree Model
In Direct Sum problems [KRW], one tries to show that for a given
computational model, the complexity of computing a collection of finite
functions on independent inputs is approximately the sum of their individual
complexities. In this paper, by contrast, we study the diversity of ways in
which the joint computational complexity can behave when all the functions are
evaluated on a common input. We focus on the deterministic decision tree model,
with depth as the complexity measure; in this model we prove a result to the
effect that the 'obvious' constraints on joint computational complexity are
essentially the only ones.
The proof uses an intriguing new type of cryptographic data structure called
a `mystery bin' which we construct using a small polynomial separation between
deterministic and unambiguous query complexity shown by Savicky. We also pose a
variant of the Direct Sum Conjecture of [KRW] which, if proved for a single
family of functions, could yield an analogous result for models such as the
communication model.Comment: Improved exposition based on conference versio
Multitask Efficiencies in the Decision Tree Model
In Direct Sum problems [KRW], one tries to show that for a given
computational model, the complexity of computing a collection of finite
functions on independent inputs is approximately the sum of their individual
complexities. In this paper, by contrast, we study the diversity of ways in
which the joint computational complexity can behave when all the functions are
evaluated on a common input. We focus on the deterministic decision tree model,
with depth as the complexity measure; in this model we prove a result to the
effect that the 'obvious' constraints on joint computational complexity are
essentially the only ones.
The proof uses an intriguing new type of cryptographic data structure called
a `mystery bin' which we construct using a small polynomial separation between
deterministic and unambiguous query complexity shown by Savicky. We also pose a
variant of the Direct Sum Conjecture of [KRW] which, if proved for a single
family of functions, could yield an analogous result for models such as the
communication model.Comment: Improved exposition based on conference versio
Restricted branching programs and hardware verification
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1995.Includes bibliographical references (p. 71-77).by Stephen John Ponzio.Ph.D