Related papers: Unification and Logarithmic Space
We present an algebraic characterization of the complexity classes Logspace and Nlogspace, using an algebra with a composition law based on unification. This new bridge between unification and complexity classes is rooted in proof theory…
We present an algebraic view on logic programming, related to proof theory and more specifically linear logic and geometry of interaction. Within this construction, a characterization of logspace (deterministic and non-deterministic)…
In a recent work, Girard proposed a new and innovative approach to computational complexity based on the proofs-as-programs correspondence. In a previous paper, the authors showed how Girard proposal succeeds in obtaining a new…
Matching logic is a logical framework for specifying and reasoning about programs using pattern matching semantics. A pattern is made up of a number of structural components and constraints. Structural components are syntactically matched,…
Logics with team semantics provide alternative means for logical characterization of complexity classes. Both dependence and independence logic are known to capture non-deterministic polynomial time, and the frontiers of tractability in…
Tremendous research effort has been dedicated over the years to thoroughly investigate non-monotonic reasoning. With the abundance of non-monotonic logical formalisms, a unified theory that enables comparing the different approaches is much…
The notion of class is ubiquitous in computer science and is central in many formalisms for the representation of structured knowledge used both in knowledge representation and in databases. In this paper we study the basic issues…
Compositionality is a key property for dealing with complexity, which has been studied from many points of view in diverse fields. Particularly, the composition of individual computations (or programs) has been widely studied almost since…
In this monograph, we study complexity classes that are defined using $O(\log n)$-space bounded non-deterministic Turing machines. We prove salient results of Computational Complexity in this topic such as the Immerman-Szelepcsenyi Theorem,…
Motivated by an ongoing project on computer aided derivation of asymptotic models governed by partial differential equations, we introduce a class of term transformations that consists of traversal strategies and insertion of contexts. We…
A number of models of linear logic are based on or closely related to linear algebra, in the sense that morphisms are "matrices" over appropriate coefficient sets. Examples include models based on coherence spaces, finiteness spaces and…
After introducing some motivations for this survey, we describe a formalism to parametrize a wide class of algebraic structures occurring naturally in various problems of topology, geometry and mathematical physics. This allows us to define…
In the paper we present results based on the description of complex systems in terms of self-organization processes of prime integer relations. Realized through the unity of two equivalent forms, i.e., arithmetical and geometrical, the…
We give an introduction to logic tailored for algebraists, explaining how proofs in linear logic can be viewed as algorithms for constructing morphisms in symmetric closed monoidal categories with additional structure. This is made explicit…
Here we define a new unification algorithm for terms interpreted in semantic domains denoted by a subclass of regular types here called deterministic regular types. This reflects our intention not to handle the semantic universe as a…
In many instances in first order logic or computable algebra, classical theorems show that many problems are undecidable for general structures, but become decidable if some rigidity is imposed on the structure. For example, the set of…
We investigate the correspondence between the time and space recognition complexity of languages. For this purpose, we will code the long-continued computations of deterministic two-tape Turing machines by the relatively short-length…
This paper investigates how global decision problems over arithmetically represented domains acquire reflective structure through class-quantification. Arithmetization forces diagonal fixed points whose verification requires reflection…
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…
Most classical results in circuit complexity theory concern circuits over the Boolean domain. Besides their simplicity and the ease of comparing different languages, the actual architecture of computers is also an important motivating…