14 research outputs found
Master index
Pla general, del mural cerĂ mic que decora una de les parets del vestĂbul de la Facultat de QuĂmica de la UB. El mural representa diversos sĂmbols relacionats amb la quĂmica
A generic imperative language for polynomial time
The ramification method in Implicit Computational Complexity has been
associated with functional programming, but adapting it to generic imperative
programming is highly desirable, given the wider algorithmic applicability of
imperative programming. We introduce a new approach to ramification which,
among other benefits, adapts readily to fully general imperative programming.
The novelty is in ramifying finite second-order objects, namely finite
structures, rather than ramifying elements of free algebras. In so doing we
bridge between Implicit Complexity's type theoretic characterizations of
feasibility, and the data-flow approach of Static Analysis.Comment: 18 pages, submitted to a conferenc
Build your own clarithmetic I: Setup and completeness
Clarithmetics are number theories based on computability logic (see
http://www.csc.villanova.edu/~japaridz/CL/ ). Formulas of these theories
represent interactive computational problems, and their "truth" is understood
as existence of an algorithmic solution. Various complexity constraints on such
solutions induce various versions of clarithmetic. The present paper introduces
a parameterized/schematic version CLA11(P1,P2,P3,P4). By tuning the three
parameters P1,P2,P3 in an essentially mechanical manner, one automatically
obtains sound and complete theories with respect to a wide range of target
tricomplexity classes, i.e. combinations of time (set by P3), space (set by P2)
and so called amplitude (set by P1) complexities. Sound in the sense that every
theorem T of the system represents an interactive number-theoretic
computational problem with a solution from the given tricomplexity class and,
furthermore, such a solution can be automatically extracted from a proof of T.
And complete in the sense that every interactive number-theoretic problem with
a solution from the given tricomplexity class is represented by some theorem of
the system. Furthermore, through tuning the 4th parameter P4, at the cost of
sacrificing recursive axiomatizability but not simplicity or elegance, the
above extensional completeness can be strengthened to intensional completeness,
according to which every formula representing a problem with a solution from
the given tricomplexity class is a theorem of the system. This article is
published in two parts. The present Part I introduces the system and proves its
completeness, while Part II is devoted to proving soundness
Modular Inference of Linear Types for Multiplicity-Annotated Arrows
Bernardy et al. [2018] proposed a linear type system as a
core type system of Linear Haskell. In the system, linearity is represented by
annotated arrow types , where denotes the multiplicity of the
argument. Thanks to this representation, existing non-linear code typechecks as
it is, and newly written linear code can be used with existing non-linear code
in many cases. However, little is known about the type inference of
. Although the Linear Haskell implementation is equipped with
type inference, its algorithm has not been formalized, and the implementation
often fails to infer principal types, especially for higher-order functions. In
this paper, based on OutsideIn(X) [Vytiniotis et al., 2011], we propose an
inference system for a rank 1 qualified-typed variant of , which
infers principal types. A technical challenge in this new setting is to deal
with ambiguous types inferred by naive qualified typing. We address this
ambiguity issue through quantifier elimination and demonstrate the
effectiveness of the approach with examples.Comment: The full version of our paper to appear in ESOP 202
Build your own clarithmetic II: Soundness
Clarithmetics are number theories based on computability logic (see
http://www.csc.villanova.edu/~japaridz/CL/ ). Formulas of these theories
represent interactive computational problems, and their "truth" is understood
as existence of an algorithmic solution. Various complexity constraints on such
solutions induce various versions of clarithmetic. The present paper introduces
a parameterized/schematic version CLA11(P1,P2,P3,P4). By tuning the three
parameters P1,P2,P3 in an essentially mechanical manner, one automatically
obtains sound and complete theories with respect to a wide range of target
tricomplexity classes, i.e. combinations of time (set by P3), space (set by P2)
and so called amplitude (set by P1) complexities. Sound in the sense that every
theorem T of the system represents an interactive number-theoretic
computational problem with a solution from the given tricomplexity class and,
furthermore, such a solution can be automatically extracted from a proof of T.
And complete in the sense that every interactive number-theoretic problem with
a solution from the given tricomplexity class is represented by some theorem of
the system. Furthermore, through tuning the 4th parameter P4, at the cost of
sacrificing recursive axiomatizability but not simplicity or elegance, the
above extensional completeness can be strengthened to intensional completeness,
according to which every formula representing a problem with a solution from
the given tricomplexity class is a theorem of the system. This article is
published in two parts. The previous Part I has introduced the system and
proved its completeness, while the present Part II is devoted to proving
soundness
Introduction to clarithmetic I
"Clarithmetic" is a generic name for formal number theories similar to Peano
arithmetic, but based on computability logic (see
http://www.cis.upenn.edu/~giorgi/cl.html) instead of the more traditional
classical or intuitionistic logics. Formulas of clarithmetical theories
represent interactive computational problems, and their "truth" is understood
as existence of an algorithmic solution. Imposing various complexity
constraints on such solutions yields various versions of clarithmetic. The
present paper introduces a system of clarithmetic for polynomial time
computability, which is shown to be sound and complete. Sound in the sense that
every theorem T of the system represents an interactive number-theoretic
computational problem with a polynomial time solution and, furthermore, such a
solution can be efficiently extracted from a proof of T. And complete in the
sense that every interactive number-theoretic problem with a polynomial time
solution is represented by some theorem T of the system. The paper is written
in a semitutorial style and targets readers with no prior familiarity with
computability logic
An Arithmetic for Non-Size-Increasing Polynomial-Time Computation
An arithmetical system is presented with the property that from every proof a realizing term can be extracted that is definable in a certain affine linear typed variant of Gödel's T and therefore defines a non-size-increasing polynomial time computable function
Proof Theory at Work: Complexity Analysis of Term Rewrite Systems
This thesis is concerned with investigations into the "complexity of term
rewriting systems". Moreover the majority of the presented work deals with the
"automation" of such a complexity analysis. The aim of this introduction is to
present the main ideas in an easily accessible fashion to make the result
presented accessible to the general public. Necessarily some technical points
are stated in an over-simplified way.Comment: Cumulative Habilitation Thesis, submitted to the University of
Innsbruc