Polynomial Invariants for Affine Programs

We exhibit an algorithm to compute the strongest polynomial (or algebraic) invariants that hold at each location of a given affine program (i.e., a program having only non-deterministic (as opposed to conditional) branching and all of whose assignments are given by affine expressions). Our main tool is an algebraic result of independent interest: given a finite set of rational square matrices of the same dimension, we show how to compute the Zariski closure of the semigroup that they generate

Twinning Automata and Regular Expressions for String Static Analysis

In this paper we formalize Tarsis, a new abstract domain based on the abstract interpretation theory that approximates string values through finite state automata. The main novelty of Tarsis is that it works over an alphabet of strings instead of single characters. On the one hand, such an approach requires a more complex and refined definition of the widening operator, and the abstract semantics of string operators. On the other hand, it is in position to obtain strictly more precise results than state-of-the-art approaches. We implemented a prototype of Tarsis, and we applied it to some case studies taken from some of the most popular Java libraries manipulating string values. The experimental results confirm that Tarsis is in position to obtain strictly more precise results than existing analyses

Certified Abstract Cost Analysis

A program containing placeholders for unspecified statements or expressions is called an abstract (or schematic) program. Placeholder symbols occur naturally in program transformation rules, as used in refactoring, compilation, optimization, or parallelization. We present a generalization of automated cost analysis that can handle abstract programs and, hence, can analyze the impact on the cost of program transformations. This kind of relational property requires provably precise cost bounds which are not always produced by cost analysis. Therefore, we certify by deductive verification that the inferred abstract cost bounds are correct and sufficiently precise. It is the first approach solving this problem. Both, abstract cost analysis and certification, are based on quantitative abstract execution (QAE) which in turn is a variation of abstract execution, a recently developed symbolic execution technique for abstract programs. To realize QAE the new concept of a cost invariant is introduced. QAE is implemented and runs fully automatically on a benchmark set consisting of representative optimization rules

Blockchain Software Verification and Optimization

In the last decade, blockchain technology has undergone a strong evolution. The maturity reached and the consolidation obtained have aroused the interest of companies and businesses, transforming it into a possible response to various industrial needs. However, the lack of standards and tools for the development and maintenance of blockchain software leaves open challenges and various possibilities for improvements. The goal of this thesis is to tackle some of the challenges proposed by blockchain technology, to design and implement analysis, processes, and architectures that may be applied in the real world. In particular, two topics are addressed: the verification of the blockchain software and the code optimization of smart contracts. As regards the verification, the thesis focuses on the original developments of tools and analyses able to detect statically, i.e. without code execution, issues related to non-determinism, untrusted cross-contracts invocation, and numerical overflow/underflow. Moreover, an approach based on on-chain verification is investigated, to proactively involve the blockchain in verifying the code before and after its deployment. For the optimization side, the thesis describes an optimization process for the code translation from Solidity language to Takamaka, also proposing an efficient algorithm to compute snapshots for fungible and non-fungible tokens. The results of this thesis are an important first step towards improving blockchain software development, empirically demonstrating the applicability of the proposed approaches and their involvement also in the industrial field

State-of-the-art on evolution and reactivity

This report starts by, in Chapter 1, outlining aspects of querying and updating resources on the Web and on the Semantic Web, including the development of query and update languages to be carried out within the Rewerse project. From this outline, it becomes clear that several existing research areas and topics are of interest for this work in Rewerse. In the remainder of this report we further present state of the art surveys in a selection of such areas and topics. More precisely: in Chapter 2 we give an overview of logics for reasoning about state change and updates; Chapter 3 is devoted to briefly describing existing update languages for the Web, and also for updating logic programs; in Chapter 4 event-condition-action rules, both in the context of active database systems and in the context of semistructured data, are surveyed; in Chapter 5 we give an overview of some relevant rule-based agents frameworks