Symbolic Logic and Mechanical Theorem Proving
Symbolic Logic and Mechanical Theorem Proving
On the lengths of proofs in the propositional calculus (Preliminary Version)
STOC '74 Proceedings of the sixth annual ACM symposium on Theory of computing
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
The polynomial hierarchy and fragments of bounded arithmetic
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
Functional interpretations of feasibly constructive arithmetic
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
A new recursion-theoretic characterization of the polytime functions (extended abstract)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
The history and status of the P versus NP question
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Examples of hard tautologies in the propositional calculus
STOC '81 Proceedings of the thirteenth annual ACM symposium on Theory of computing
Propositional representation of arithmetic proofs (Preliminary Version)
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Some connections between mathematical logic and complexity theory
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
The consistency of "P = NP" and related problems with fragments of number theory
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
Theories with self-application and computational complexity
Information and Computation
Resolution and binary decision diagrams cannot simulate each other polynomially
Discrete Applied Mathematics - The renesse issue on satisfiability
Automated higher-order complexity analysis
Theoretical Computer Science - Implicit computational complexity
The strength of replacement in weak arithmetic
ACM Transactions on Computational Logic (TOCL)
Gödel and computations: a 100th anniversary retrospective
ACM SIGACT News
Many Facets of Complexity in Logic
CiE '08 Proceedings of the 4th conference on Computability in Europe: Logic and Theory of Algorithms
A Tight Karp-Lipton Collapse Result in Bounded Arithmetic
CSL '08 Proceedings of the 22nd international workshop on Computer Science Logic
Dynamic Symmetry Breaking by Simulating Zykov Contraction
SAT '09 Proceedings of the 12th International Conference on Theory and Applications of Satisfiability Testing
Characterizing the Existence of Optimal Proof Systems and Complete Sets for Promise Classes
CSR '09 Proceedings of the Fourth International Computer Science Symposium in Russia on Computer Science - Theory and Applications
Logical closure properties of propositional proof systems
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
A tight Karp-Lipton collapse result in bounded arithmetic
ACM Transactions on Computational Logic (TOCL)
On approximate horn formula minimization
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
From feasible proofs to feasible computations
CSL'10/EACSL'10 Proceedings of the 24th international conference/19th annual conference on Computer science logic
Higher complexity search problems for bounded arithmetic and a formalized no-gap theorem
Archive for Mathematical Logic
A propositional proof system for log space
CSL'05 Proceedings of the 19th international conference on Computer Science Logic
Complexity of propositional proofs
CSR'10 Proceedings of the 5th international conference on Computer Science: theory and Applications
A note on SAT algorithms and proof complexity
Information Processing Letters
| Hi-index | 0.00 |
The motivation for this work comes from two general sources. The first source is the basic open question in complexity theory of whether P equals NP (see [1] and [2]). Our approach is to try to show they are not equal, by trying to show that the set of tautologies is not in NP (of course its complement is in NP). This is equivalent to showing that no proof system (in the general sense defined in [3]) for the tautologies is “super” in the sense that there is a short proof for every tautology. Extended resolution is an example of a powerful proof system for tautologies that can simulate most standard proof systems (see [3]). The Main Theorem (5.5) in this paper describes the power of extended resolution in a way that may provide a handle for showing it is not super. The second motivation comes from constructive mathematics. A constructive proof of, say, a statement @@@@×A must provide an effective means of finding a proof of A for each value of x, but nothing is said about how long this proof is as a function of x. If the function is exponential or super exponential, then for short values of x the length of the proof of the instance of A may exceed the number of electrons in the universe. In section 2, I introduce the system PV for number theory, and it is this system which I suggest properly formalizes the notion of a feasibly constructive proof.