4 research outputs found
Unrestricted Termination and Non-Termination Arguments for Bit-Vector Programs
Proving program termination is typically done by finding a well-founded
ranking function for the program states. Existing termination provers typically
find ranking functions using either linear algebra or templates. As such they
are often restricted to finding linear ranking functions over mathematical
integers. This class of functions is insufficient for proving termination of
many terminating programs, and furthermore a termination argument for a program
operating on mathematical integers does not always lead to a termination
argument for the same program operating on fixed-width machine integers. We
propose a termination analysis able to generate nonlinear, lexicographic
ranking functions and nonlinear recurrence sets that are correct for
fixed-width machine arithmetic and floating-point arithmetic Our technique is
based on a reduction from program \emph{termination} to second-order
\emph{satisfaction}. We provide formulations for termination and
non-termination in a fragment of second-order logic with restricted
quantification which is decidable over finite domains. The resulted technique
is a sound and complete analysis for the termination of finite-state programs
with fixed-width integers and IEEE floating-point arithmetic
Program Synthesis for Program Analysis
In this article, we propose a unified framework for designing static analysers based on program synthesis. For this purpose, we identify a fragment of second-order logic with restricted quantification that is expressive enough to model numerous static analysis problems (e.g., safety proving, bug finding, termination and non-termination proving, refactoring). As our focus is on programs that use bit-vectors, we build a decision procedure for this fragment over finite domains in the form of a program synthesiser. We provide instantiations of our framework for solving a diverse range of program verification tasks such as termination, non-termination, safety and bug finding, superoptimisation, and refactoring. Our experimental results show that our program synthesiser compares positively with specialised tools in each area as well as with general-purpose synthesisers
Program Synthesis for Program Analysis
In this paper, we propose a unified framework for designing static analysers based on program synthesis. For this purpose, we identify a fragment of second-order logic with restricted quantification that is expressive enough to model numerous static analysis problems (e.g., safety proving, bug finding, termination and non-termination proving, refactoring). As our focus is on programs that use bit-vectors, we build a decision procedure for this fragment over finite domains in the form of a program synthesiser. We provide instantiations of our framework for solving a diverse range of program verification tasks such as termination, non-termination, safety and bug finding, superoptimisation and refactoring. Our experimental results show that our program synthesiser
compares positively with specialised tools in each area as well as with general-purpose synthesisers
Termination of Narrowing: Automated Proofs and Modularity Properties
En 1936 Alan Turing demostro que el halting problem, esto es, el problema de decidir
si un programa termina o no, es un problema indecidible para la inmensa mayoria de
los lenguajes de programacion. A pesar de ello, la terminacion es un problema tan
relevante que en las ultimas decadas un gran numero de tecnicas han sido desarrolladas
para demostrar la terminacion de forma automatica de la maxima cantidad posible de
programas. Los sistemas de reescritura de terminos proporcionan un marco teorico
abstracto perfecto para el estudio de la terminacion de programas. En este marco, la
evaluaci on de un t ermino consiste en la aplicacion no determinista de un conjunto de
reglas de reescritura.
El estrechamiento (narrowing) de terminos es una generalizacion de la reescritura
que proporciona un mecanismo de razonamiento automatico. Por ejemplo, dado un
conjunto de reglas que denan la suma y la multiplicacion, la reescritura permite calcular
expresiones aritmeticas, mientras que el estrechamiento permite resolver ecuaciones
con variables. Esta tesis constituye el primer estudio en profundidad de las
propiedades de terminacion del estrechamiento. Las contribuciones son las siguientes.
En primer lugar, se identican clases de sistemas en las que el estrechamiento tiene
un comportamiento bueno, en el sentido de que siempre termina. Muchos metodos
de razonamiento automatico, como el analisis de la semantica de lenguajes de programaci
on mediante operadores de punto jo, se benefician de esta caracterizacion.
En segundo lugar, se introduce un metodo automatico, basado en el marco teorico
de pares de dependencia, para demostrar la terminacion del estrechamiento en un
sistema particular. Nuestro metodo es, por primera vez, aplicable a cualquier clase
de sistemas.
En tercer lugar, se propone un nuevo metodo para estudiar la terminacion del
estrechamiento desde un termino particular, permitiendo el analisis de la terminacion
de lenguajes de programacion. El nuevo metodo generaliza losIborra López, J. (2010). Termination of Narrowing: Automated Proofs and Modularity Properties [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/19251Palanci