Related papers: S-Program Calculus
Sound over-approximation methods have been proved effective for guaranteeing the absence of errors, but inevitably they produce false alarms that can hamper the programmers. Conversely, under-approximation methods are aimed at bug finding…
We present a formal system for proving the partial correctness of a single-pass instruction sequence as considered in program algebra by decomposition into proofs of the partial correctness of segments of the single-pass instruction…
In this paper, a Gaifman-Shapiro-style module architecture is tailored to the case of Smodels programs under the stable model semantics. The composition of Smodels program modules is suitably limited by module conditions which ensure the…
The overall goal of this paper is to investigate the theoretical foundations of algorithmic verification techniques for first order linear logic specifications. The fragment of linear logic we consider in this paper is based on the linear…
In this work, we consider the almost-sure termination problem for probabilistic programs that asks whether a given probabilistic program terminates with probability 1. Scalable approaches for program analysis often rely on modularity as…
Completeness of a logic program means that the program produces all the answers required by its specification. The cut is an important construct of programming language Prolog. It prunes part of the search space, this may result in a loss…
We study the problem of completely automatically verifying uninterpreted programs---programs that work over arbitrary data models that provide an interpretation for the constants, functions and relations the program uses. The verification…
We define a class of computable functions over real numbers using functional schemes similar to the class of primitive and partial recursive functions defined by G\"odel and Kleene. We show that this class of functions can also be…
Computer Algebra systems are widely spread because of some of their remarkable features such as their ease of use and performance. Nonetheless, this focus on performance sometimes leads to unwanted consequences: algorithms and computations…
In this paper, we study the provability logic of intuitionistic theories of arithmetic that prove their own completeness. We prove a completeness theorem for theories equipped with two provability predicates $\Box$ and $\triangle$ that…
Let R be a complete discrete valuation ring, S=R[[u]] and n a positive integer. The aim of this paper is to explain how to compute efficiently usual operations such as sum and intersection of sub-S-modules of S^d. As S is not principal, it…
Argumentation problems are concerned with determining the acceptability of a set of arguments from their relational structure. When the available information is uncertain, probabilistic argumentation frameworks provide modelling tools to…
Specification languages are essential in deductive program verification, but they are usually based on first-order logic, hence less expressive than the programs they specify. Recently, trace specification logics with fixed points that are…
In deductive verification and software model checking, dealing with certain specification language constructs can be problematic when the back-end solver is not sufficiently powerful or lacks the required theories. One way to deal with this…
A classical result by Floyd ("On the non-existence of a phrase structure grammar for ALGOL 60", 1962) states that the complete syntax of any sensible programming language cannot be described by the ordinary kind of formal grammars…
Computability logic (CoL) (see http://www.cis.upenn.edu/~giorgi/cl.html) is a recently introduced semantical platform and ambitious program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth…
Auto-active program verification rests on the ability to effectively the translation from annotated programs into verification conditions that are then discharged by automated theorem provers in the background. Characteristic such tools,…
Hoare-style verification provides a principled foundation for reasoning about the correctness of quantum programs, but existing approaches do not allow fully automatic verification. While automata-based verification scales well when…
Many important functional and security properties--including non-interference, determinism, and generalized non-interference (GNI)--are hyperproperties, i.e., properties relating multiple executions of a program. Existing separation logics…
We propose a new approach to formally describing the requirement for statistical inference and checking whether a program uses the statistical method appropriately. Specifically, we define belief Hoare logic (BHL) for formalizing and…