## 18 Citations

### Non-Linear Time Lower Bound for (Succinct) Quantified Boolean Formulas

- Computer Science, MathematicsElectron. Colloquium Comput. Complex.
- 2008

This work gives a reduction from arbitrary languages in alternating time t(n) to QBFs describable in O(t(n)) bits by a reasonable (polynomially) succinct encoding, and proves that the succinct QBF problem requires superlinear time on those models.

### Inductive Time-Space Lower Bounds for Sat and Related Problems

- Computer Science, Mathematicscomputational complexity
- 2007

It is proved that for all k ≥ 1, there is a constant ck > 1 such that linear time with n1/k nondeterministic bits is not contained in deterministic time, used to prove that satisfiability of Boolean circuits with n inputs and nk size cannot be solved by deterministic multitape Turing machines.

### One-Tape Turing Machine and Branching Program Lower Bounds for MCSP

- Computer ScienceElectron. Colloquium Comput. Complex.
- 2020

These results are the first non-trivial lower bounds for MCSP and MKTP against one-tape Turing machines and non-deterministic branching programs, and essentially match the best-known lower bound for any explicit functions against these computational models.

### Pseudorandom bits and lower bounds for randomized Turing machines

- Computer ScienceElectron. Colloquium Comput. Complex.
- 2019

A pseudorandom generator with nearly quadratic stretch for randomized Turing machines, which have a one-way random tape and a two-way work tape, and is used to prove a time lower bound for a function computable in linear time with two quantiﬁer alternations.

### Algorithms and resource requirements for fundamental problems

- Computer Science, Mathematics
- 2007

It is proved that the Boolean satisfiability problem and other hard problems require Ω(n2cos(π/7)- o(1)) ≥Ω( n1.801) time to solve by any algorithm that uses no(1) space, and more efficient methods for solving interesting classes of NP-hard problems exactly are established.

### Automated Proofs of Time Lower Bounds

- Computer Science
- 2007

It is proved that the search for better lower bounds can often be turned into a problem of solving a large series of linear programming instances, and an automated theorem-proving methodology is proposed for studying these lower bound problems.

### Better time-space lower bounds for SAT and related problems

- Computer Science20th Annual IEEE Conference on Computational Complexity (CCC'05)
- 2005

An elementary technique based on "indirect diagonalization" that uniformly improves upon the known nonlinear time lower bounds for nondeterminism and alternating computation, on both sublinear space RAMs and sequential worktape machines with random access to the input.

### Time-space lower bounds for satisfiability

- Computer ScienceJACM
- 2005

We establish the first polynomial time-space lower bounds for satisfiability on general models of computation. We show that for any constant <i>c</i> less than the golden ratio there exists a…

### On Approximate Majority and Probabilistic Time

- Computer Science, MathematicsTwenty-Second Annual IEEE Conference on Computational Complexity (CCC'07)
- 2007

It is proved that depth-3 circuits with bottom fan-in (log n)/2 that compute approximate majority on n bits must have size at least 2 n 0.1, and there is no black-box proof that BPTime (t) is computable by uniform polynomial-size circuits of depth 3.

### Alternation-Trading Proofs, Linear Programming, and Lower Bounds

- Computer Science, Mathematics
- 2018

It is proved that the search for better lower bounds can often be turned into a problem of solving a large series of linear programming instances, and new human-readable time lower bounds for several problems are extracted.

## References

SHOWING 1-10 OF 17 REFERENCES

### Matching upper and lower bounds for simulations of several linear tapes on one multidimensional tape

- Computer Sciencecomputational complexity
- 1999

A matching lower bound is proved which holds for the problem of recognizing languages on machines with a separate one-way input tape for Turing machines using one d-dimensional work tape.

### Matching Upper and Lower Bounds for Simulation of Several Tapes on One Multidimensional Tape

- Computer ScienceFSTTCS
- 1994

We prove a \(\Theta (t(n)\sqrt[d]{{t(n)}}/\log i(n))\) bound for the simulation of t(n) steps of a Turing machine using several one-dimensional work tapes on a Turing machine using one d-dimensional…

### On the complexity of SAT

- Computer Science, Mathematics40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039)
- 1999

We show that non-deterministic time NTIME(n) is not contained in deterministic time n/sup 2-/spl epsiv// and polylogarithmic space, for any /spl epsiv/>0. This implies that (infinitely often),…

### A hierarchy for nondeterministic time complexity

- Computer ScienceJ. Comput. Syst. Sci.
- 1973

For any real numbers r1, r2, 1 ≤ r1 < r2 , there is a set A of strings which has nondeterministic time complexity nr2 but not nondeterdependencies nr1, and the computing devices are non-deterministic multitape Turing machines.

### Two tapes versus one for off-line Turing machines

- Computer Sciencecomputational complexity
- 2005

We prove the first superlinear lower bound for a concrete, polynomial time recognizable decision problem on a Turing machine with one work tape and a two-way input tape (also called off-line 1-tape…

### Time-Space Tradeoffs for Satisfiability

- Computer Science, MathematicsJ. Comput. Syst. Sci.
- 2000

It is shown that SAT cannot be solved in n1+o(1) time and n1?? space for any general random-access nondeterministic Turing machines, and lower bounds for log-space uniform NC1 circuits and branching programs are given.

### Short Propositional Formulas Represent Nondeterministic Computations

- Computer ScienceInf. Process. Lett.
- 1988

### Time-space tradeoffs for nondeterministic computation

- Computer ScienceProceedings 15th Annual IEEE Conference on Computational Complexity
- 2000

In general, for any constant a less than the golden ratio, it is proved that satisfiability cannot be solved in time n/sup a/ and space n/Sup /spl delta// for some positive constant b.

### Time-space lower bounds for satisfiability

- Computer ScienceJACM
- 2005

We establish the first polynomial time-space lower bounds for satisfiability on general models of computation. We show that for any constant <i>c</i> less than the golden ratio there exists a…