Related papers: On the computational complexity of cut-reduction
Cut-elimination is the bedrock of proof theory with a multitude of applications from computational interpretations to proof analysis. It is also the starting point for important meta-theoretical investigations including decidability,…
It has been argued that reduction procedures are closely connected to the question about identity of proofs and that accepting certain reductions would lead to a trivialization of identity of proofs in the sense that every derivation of the…
Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…
Although there is a somewhat standard formalization of computability on countable sets given by Turing machines, the same cannot be said about uncountable sets. Among the approaches to define computability in these sets, order-theoretic…
In this paper, we present a comprehensive system for the treatment of the topic of limits--conceptually, computationally, and formally. The system addresses fundamental linguistic flaws in the standard presentation of limits, which attempts…
We present a comprehensive programme analysing the decomposition of proof systems for non-classical logics into proof systems for other logics, especially classical logic, using an algebra of constraints. That is, one recovers a proof…
We introduce a non-wellfounded proof system for intuitionistic logic extended with inductive and co-inductive definitions, based on a syntax in which fixpoint formulas are annotated with explicit variables for ordinals. We explore the…
A term calculus for the proofs in multiplicative-additive linear logic is introduced and motivated as a programming language for channel based concurrency. The term calculus is proved complete for a semantics in linearly distributive…
The depth-bounded fragment of the pi-calculus is an expressive class of systems enjoying decidability of some important verification problems. Unfortunately membership of the fragment is undecidable. We propose a novel type system,…
A typical way of analyzing the time complexity of functional programs is to extract a recurrence expressing the running time of the program in terms of the size of its input, and then to solve the recurrence to obtain a big-O bound. For…
What is computable with limited resources? How can we verify the correctness of computations? How to measure computational power with precision? Despite the immense scientific and engineering progress in computing, we still have only…
Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…
We define a proof system for exceptions which is close to the syntax for exceptions, in the sense that the exceptions do not appear explicitly in the type of any expression. This proof system is sound with respect to the intended…
We survey results on the formalization and independence of mathematical statements related to major open problems in computational complexity theory. Our primary focus is on recent findings concerning the (un)provability of complexity…
Many applications of denotational semantics, such as higher-order model checking or the complexity of normalization, rely on finite semantics for monomorphic type systems. We exhibit such a finite semantics for a polymorphic purely linear…
The field of computational complexity is concerned both with the intrinsic hardness of computational problems and with the efficiency of algorithms to solve them. Given such a problem, normally one designs an algorithm to solve it and sets…
The paper proposes a theoretical approach of the debugging of constraint programs based on a notion of explanation tree. The proposed approach is an attempt to adapt algorithmic debugging to constraint programming. In this theoretical…
Combining a standard proof search method, such as resolution or tableaux, and rewriting is a powerful way to cut off search space in automated theorem proving, but proving the completeness of such combined methods may be challenging. It may…
Cut-elimination is the bedrock of proof theory. It is the algorithm that eliminates cuts from a sequent calculus proof that leads to cut-free calculi and applications. Cut-elimination applies to many logics irrespective of their semantics.…
It is known that any rational abstract numeration system is faithfully, and effectively, represented by an N-rational series. A simple proof of this result is given which yields a representation of this series which in turn allows a simple…