DeepAI
Log In Sign Up

A Rice's Theorem for Abstract Semantics

05/30/2021
by   Paolo Baldan, et al.
0

Classical results in computability theory, notably Rice's theorem, focus on the extensional content of programs, namely, on the partial recursive functions that programs compute. Later and more recent work investigated intensional generalisations of such results that take into account the way in which functions are computed, thus affected by the specific programs computing them. In this paper, we single out a novel class of program semantics based on abstract domains of program properties that are able to capture nonextensional aspects of program computations, such as their asymptotic complexity or logical invariants, and allow us to generalise some foundational computability results such as Rice's Theorem and Kleene's Second Recursion Theorem to these semantics. In particular, it turns out that for this class of abstract program semantics, any nontrivial abstract property is undecidable and every decidable overapproximation necessarily includes an infinite set of false positives which covers all values of the semantic abstract domain.

READ FULL TEXT

page 1

page 3

page 5

page 9

page 13

page 23

page 29

page 33

02/12/2021

On Signings and the Well-Founded Semantics

In this note, we use Kunen's notion of a signing to establish two theore...
12/26/2017

On the Semantics of Intensionality and Intensional Recursion

Intensionality is a phenomenon that occurs in logic and computation. In ...
09/15/2018

Neural Networks as Artificial Specifications

In theory, a neural network can be trained to act as an artificial speci...
07/18/2019

On the Monniaux Problem in Abstract Interpretation

The Monniaux Problem in abstract interpretation asks, roughly speaking, ...
07/13/2020

Generating Functions for Probabilistic Programs

This paper investigates the usage of generating functions (GFs) encoding...
05/15/2021

Delay-Bounded Scheduling Without Delay! (Extended Technical Report)

We consider the broad problem of analyzing safety properties of asynchro...
03/02/2021

Dynamic Verification of C/C++11 Concurrency over Multi Copy Atomics

We investigate the problem of runtime analysis of C11 programs under Mul...