# A Linear-Time Algorithm for Testing the Truth of Certain Quantified Boolean Formulas

@article{Aspvall1979ALA,
title={A Linear-Time Algorithm for Testing the Truth of Certain Quantified Boolean Formulas},
author={Bengt Aspvall and Michael F. Plass and Robert E. Tarjan},
journal={Inf. Process. Lett.},
year={1979},
volume={8},
pages={121-123}
}
• Published 15 March 1979
• Mathematics
• Inf. Process. Lett.
896 Citations

## Figures from this paper

On 2-QBF Truth Testing in Parallel
• Philosophy
Inf. Process. Lett.
• 1996
• K. Subramani
• Mathematics, Computer Science
Int. J. Found. Comput. Sci.
• 2005
This work proposes an incremental, randomized approach for the Q2SAT problem that is essentially local in nature, in that the complete clausal set need not be provided at any time, in the presence of a verifier.
Finding almost-satisfying assignments
It is shown that ZSAT and HORN-SAT are, essentially, the only non-trivial classes of formulae for which almost-satisfying assignments can be found in polynomial time (assuming P # NP).
A simplifier for propositional formulas with many binary clauses
• R. Brafman
• Computer Science
IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics)
• 2004
Experimental evaluation of this formula simplifier on a number of bench-mark formulas produced by encoding AI planning problems prove 2-SIMPLIFY to be a useful tool in many circumstances.
Deciding the Satisfiability of Propositional Formulas in Finitely-Valued Signed Logics
• Computer Science
38th International Symposium on Multiple Valued Logic (ismvl 2008)
• 2008
This paper considers propositional, finitely-valued formulas in clausal normal form, and presents a polynomial-time algorithm for deciding whether a given set of signs satisfies the Helly property.
Density condensation of Boolean formulas
• Mathematics, Computer Science
Discret. Appl. Math.
• 2003
On the Complexity of the CQF Hierarchy
The complexity of two subclasses of Constrained Quantified Formula, Horn and 2CNF, is determined and the complexity of Horn CQF(i) is reduced by one level in the polynomial hierarchy.
On Boolean Models for Quantified Boolean Horn Formulas
• Philosophy
SAT
• 2003
It is shown that any true quantified Horn formula has a Boolean model consisting of monotone monomials and constant functions only; conversely, if a QBF has such a model then it contains a clause–subformula in $${\it QHORN }\cap {\it SAT }$$.

## References

SHOWING 1-9 OF 9 REFERENCES
The complexity of satisfiability problems
An infinite class of satisfiability problems is considered which contains these two particular problems as special cases, and it is shown that every member of this class is either polynomial-time decidable or NP-complete.
The complexity of theorem-proving procedures
• S. Cook
• Mathematics, Computer Science
STOC
• 1971
It is shown that any recognition problem solved by a polynomial time-bounded nondeterministic Turing machine can be “reduced” to the problem of determining whether a given propositional formula is a
On the complexity of time table and multi-commodity flow problems
• Computer Science
16th Annual Symposium on Foundations of Computer Science (sfcs 1975)
• 1975
The theorem that a meeting function always exists if all teachers and classes have no time constraints is proved and the multi-commodity integral flow problem is shown to be NP-complete even if the number of commodities is two.
Depth-First Search and Linear Graph Algorithms
The value of depth-first search or “backtracking” as a technique for solving problems is illustrated by two examples. An improved version of an algorithm for finding the strongly connected components
On the Complexity of Timetable and Multicommodity Flow Problems
• Computer Science
SIAM J. Comput.
• 1976
A very primitive version of Gotlieb’s timetable problem is shown to be NP-complete, and therefore all the common timetable problems are NP-complete. A polynomial time algorithm, in case all teachers
The Design and Analysis of Computer Algorithms
• Computer Science
• 1974
This text introduces the basic data structures and programming techniques often used in efficient algorithms, and covers use of lists, push-down stacks, queues, trees, and graphs.
CombinatoriaI Algorithms: Theory and Practice
• CombinatoriaI Algorithms: Theory and Practice
• 1977
Word problems requiring exponential time
• Proc. 5th Ann
• 1973