4 research outputs found
On Time Versus Space III
Coordinated Science Laboratory was formerly known as Control Systems LaboratoryNational Science Foundation / MCS-8217445 and MCS-7719754Eastman Kodak CompanyFannie and John Hertz Foundatio
Alternation-Trading Proofs, Linear Programming, and Lower Bounds
A fertile area of recent research has demonstrated concrete polynomial time
lower bounds for solving natural hard problems on restricted computational
models. Among these problems are Satisfiability, Vertex Cover, Hamilton Path,
Mod6-SAT, Majority-of-Majority-SAT, and Tautologies, to name a few. The proofs
of these lower bounds follow a certain proof-by-contradiction strategy that we
call alternation-trading. An important open problem is to determine how
powerful such proofs can possibly be.
We propose a methodology for studying these proofs that makes them amenable
to both formal analysis and automated theorem proving. We prove that the search
for better lower bounds can often be turned into a problem of solving a large
series of linear programming instances. Implementing a small-scale theorem
prover based on this result, we extract new human-readable time lower bounds
for several problems. This framework can also be used to prove concrete
limitations on the current techniques.Comment: To appear in STACS 2010, 12 page
On parallel Turing machines with multi-head control units
This paper deals with parallel Turing machines with multi-head
control units on one or more tapes which can be considered as a
generalization of cellular automata. We discuss the problem of
finding an appropriate measure of space complexity. A definition is
suggested which implies that the model is in the first machine
class. It is shown that without loss of generality it suffices to
consider only parallel Turing machines of certain normal forms
Hierarchies and Space Measures for Pointer Machines
Coordinated Science Laboratory was formerly known as Control Systems LaboratoryAir Force Institute of Technology, AFIT/CIR