Bounded Arithmetic and Descriptive Complexity
نویسنده
چکیده
We study definability of languages in arithmetic and the free monoid by bounded versions of fixed-point and transitive-closure logics. In particular we give logical characterisations of complexity classes C by showing that a language belongs to C if and only if it is definable in either arithmetic or the free monoid by a formula of a certain logic. We investigate in which cases the bounds of fixed-point operators may be omitted. Finally, a general translation of results from descriptive complexity to the approach described in this paper is presented.
منابع مشابه
Closure Properties of Weak Systems of Bounded Arithmetic
In this paper we study the properties of systems of bounded arithmetic capturing small complexity classes and state conditions sufficient for such systems to capture the corresponding complexity class tightly. Our class of systems of bounded arithmetic is the class of secondorder systems with comprehension axiom for a syntactically restricted class of formulas Φ ⊂ Σ 1 based on a logic in the de...
متن کاملCuts and overspill properties in models of bounded arithmetic
In this paper we are concerned with cuts in models of Samuel Buss' theories of bounded arithmetic, i.e. theories like $S_{2}^i$ and $T_{2}^i$. In correspondence with polynomial induction, we consider a rather new notion of cut that we call p-cut. We also consider small cuts, i.e. cuts that are bounded above by a small element. We study the basic properties of p-cuts and small cuts. In particula...
متن کاملA Finite-Model-Theoretic View on Propositional Proof Complexity
We establish new, and surprisingly tight, connections between propositional proof complexity and finite model theory. Specifically, we show that the power of several propositional proof systems, such as Horn resolution, bounded-width resolution, and the polynomial calculus of bounded degree, can be characterised in a precise sense by variants of fixed-point logics that are of fundamental import...
متن کاملThe Model-Theoretic Expressiveness of Propositional Proof Systems
We establish new, and surprisingly tight, connections between propositional proof complexity and finite model theory. Specifically, we show that the power of several propositional proof systems, such as Horn resolution, bounded width resolution, and the polynomial calculus of bounded degree, can be characterised in a precise sense by variants of fixed-point logics that are of fundamental import...
متن کاملProofs, Programs and Abstract Complexity
Axiom systems are ubiquitous in mathematical logic, one famous and well studied example being first order Peano arithmetic. Foundational questions asked about axiom systems comprise analysing their provable consequences, describing their class of provable recursive functions (i.e. for which programs can termination be proven from the axioms), and characterising their consistency strength. One b...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2000