The computational complexity of constraint satisfaction problems that are based on integer expressions and algebraic circuits, such as L, P, NP, PSPACE, NEXP, and even Sigma_1, the class of c.e. languages, is studied.Expand

It turns out that the following problems are equivalent to PIT, which shows that the challenge to improve their bounds is just a reformulation of a major open problem in algebraic computing complexity.Expand

The article investigates the relation between three well-known hypotheses, Hunion, Hopps and Hcpair, and characterizations of Hunion and two variants in terms of coNP-completeness and pproducibility of the set of hard formulas of propositional proof systems are obtained.Expand

An oracle is constructed relative to which no many-one complete disjoint NP-pairs exist and each problem in NP has P-optimal proof systems, showing that there is no relativizable proof for $\mathsf{DisjNP} \Rightarrow \Mathsf{SAT}$.Expand

The work shows that the balance problem for { ∖, ⋅ } -circuits is undecidable which is the first natural problem for integer circuits or related constraint satisfaction problems that admits only one arithmetic operation and is proven to be Undecidable.Expand

There is no relativizable proof for the implication DisjNP ∧ UP ∧ NP ∩ coNP ⇒ SAT, so an oracle is constructed relative to which Disj NP, ¬ SAT, UP, and NP ∪ coNP hold.Expand

The work shows that the balance problem for {−, ·}-circuits is undecidable which is the first natural problem for integer circuits or related constraint satisfaction problems that admits only one arithmetic operation and is proven to be Undecidable.Expand

An oracle is constructed relative to which there is no relativizable proof for the implication that NP does not contain many-one complete sets that have P-optimal proof systems.Expand