Lower Bounds for Polynomial Calculus: Non-Binomial Case
نویسندگان
چکیده
We generalize recent linear lower bounds for Polynomial Calculus based on binomial ideals. We produce a general hardness criterion (that we call immunity) which is satisfied by a random function and prove linear lower bounds on the size of PC refutations for a wide class of tautologies based on immune functions. As some applications of our techniques, we introduce modp Tseitin tautologies in the Boolean case (e.g. in the presence of axioms xi = xi), prove that they are hard for PC over fields with characteristic different from p, and generalize them to Flow tautologies which are based on the MAJORITY function and are proved to be hard over any field. We also show the Ω(n) lower bound for random k-CNF’s over fields of characteristic 2.
منابع مشابه
NON-POLYNOMIAL SPLINE FOR THE NUMERICAL SOLUTION OF PROBLEMS IN CALCULUS OF VARIATIONS
A Class of new methods based on a septic non-polynomial spline function for the numerical solution of problems in calculus of variations is presented. The local truncation errors and the methods of order 2th, 4th, 6th, 8th, 10th, and 12th, are obtained. The inverse of some band matrixes are obtained which are required in proving the convergence analysis of the presented method. Convergence anal...
متن کاملOn Complexity Measures in Polynomial Calculus
Proof complexity is the study of non-deterministic computational models, called proof systems, for proving that a given formula of propositional logic is unsatisfiable. As one of the subfields of computational complexity theory, the main questions of study revolve around the amount of resources needed to prove the unsatisfiability of various formulas in different proof systems. This line of inq...
متن کاملLower Bounds for a Proof System with an Expentential Speed-up over Constant-Depth Frege Systems and over Polynomial Calculus
We prove lower bounds for a proof system having exponential speed-up over both polynomial calculus and constant-depth Frege systems in DeMorgan language.
متن کاملBounds on certain classes of Kronecker and q-binomial coefficients
We present a lower bound on the Kronecker coefficients for tensor squares of the symmetric group via the characters of Sn, which we apply to obtain various explicit estimates. Notably, we extend Sylvester’s unimodality of q-binomial coefficients ( n k ) q as polynomials in q to derive sharp bounds on the differences of their consecutive coefficients. We then derive effective asymptotic lower bo...
متن کاملBOUNDS ON KRONECKER AND q-BINOMIAL COEFFICIENTS
We present a lower bound on the Kronecker coefficients of the symmetric group via the characters of Sn, which we apply to obtain various explicit estimates. Notably, we extend Sylvester’s unimodality of q-binomial coefficients ( n k ) q as polynomials in q to derive sharp bounds on the differences of their consecutive coefficients.
متن کامل