Universal First-Order Logic is Superfluous for NL, P, NP and coNP

In this work we continue the syntactic study of completeness that began with the works of Immerman and Medina. In particular, we take a conjecture raised by Medina in his dissertation that says if a conjunction of a second-order and a first-order sentences defines an NP-complete problems via fops, then it must be the case that the second-order conjoint alone also defines a NP-complete problem. Although this claim looks very plausible and intuitive, currently we cannot provide a definite answer for it. However, we can solve in the affirmative a weaker claim that says that all ``consistent'' universal first-order sentences can be safely eliminated without the fear of losing completeness. Our methods are quite general and can be applied to complexity classes other than NP (in this paper: to NLSPACE, PTIME, and coNP), provided the class has a complete problem satisfying a certain combinatorial property

Program schemes with deep pushdown storage.

Inspired by recent work of Meduna on deep pushdown automata, we consider the computational power of a class of basic program schemes, TeX, based around assignments, while-loops and non- deterministic guessing but with access to a deep pushdown stack which, apart from having the usual push and pop instructions, also has deep-push instructions which allow elements to be pushed to stack locations deep within the stack. We syntactically define sub-classes of TeX by restricting the occurrences of pops, pushes and deep-pushes and capture the complexity classes NP and PSPACE. Furthermore, we show that all problems accepted by program schemes of TeX are in EXPTIME

A Constant-Space Sequential Model of Computation for First-Order Logic

AbstractWe define and justify a natural sequential model of computation with a constant amount of read/write work space, despite unlimited (polynomial) access to read-only input and write-only output. The model is deterministic, uniform, and sequential. The constant work space is modeled by a finite number of destructively read boolean variables, assignable by formulas over the canonical boolean operations. We show that computation on this model is equivalent to expressibility in first-order logic, giving a duality between (read-once) constant-space serial algorithms and constant-time parallel algorithms