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Bishoksan Kafle

Publications and source records attributed to Bishoksan Kafle.

15 recordsLinked to original sources
arXiv2021

Regular Path Clauses and Their Application in Solving Loops

A well-established approach to reasoning about loops during program analysis is to capture the effect of a loop by extracting recurrences from the loop; these express relationships between the values of variables, or program properties such as cost, on successive loop iterations. Recurrence solvers are capable of computing closed forms for some recurrences, thus deriving precise relationships capturing the complete loop execution. However, many recurrences extracted from loops cannot be solved, due to their having multiple recursive cases or multiple arguments. In the literature, several techniques for approximating the solution of unsolvable recurrences have been proposed. The approach presented in this paper is to define transformations based on regular path expressions and loop counters that (i) transform multi-path loops to single-path loops, giving rise to recurrences with a single recursive case, and (ii) transform multi-argument recurrences to single-argument recurrences, thus enabling the use of recurrence solvers on the transformed recurrences. Using this approach, precise solutions can sometimes be obtained that are not obtained by approximation methods.

cs.LO↗
arXiv2021

Transformation-Enabled Precondition Inference

Precondition inference is a non-trivial problem with important applications in program analysis and verification. We present a novel iterative method for automatically deriving preconditions for the safety and unsafety of programs. Each iteration maintains over-approximations of the set of safe and unsafe initial states; which are used to partition the program's initial states into those known to be safe, known to be unsafe and unknown. We then construct revised programs with those unknown initial states and iterate the procedure until the approximations are disjoint or some termination criteria are met. An experimental evaluation of the method on a set of software verification benchmarks shows that it can infer precise preconditions (sometimes optimal) that are not possible using previous methods.

cs.PL↗
arXiv2020

From Big-Step to Small-Step Semantics and Back with Interpreter Specialisation

We investigate representations of imperative programs as constrained Horn clauses. Starting from operational semantics transition rules, we proceed by writing interpreters as constrained Horn clause programs directly encoding the rules. We then specialise an interpreter with respect to a given source program to achieve a compilation of the source language to Horn clauses (an instance of the first Futamura projection). The process is described in detail for an interpreter for a subset of C, directly encoding the rules of big-step operational semantics for C. A similar translation based on small-step semantics could be carried out, but we show an approach to obtaining a small-step representation using a linear interpreter for big-step Horn clauses. This interpreter is again specialised to achieve the translation from big-step to small-step style. The linear small-step program can be transformed back to a big-step non-linear program using a third interpreter. A regular path expression is computed for the linear program using Tarjan's algorithm, and this regular expression then guides an interpreter to compute a program path. The transformation is realised by specialisation of the path interpreter. In all of the transformation phases, we use an established partial evaluator and exploit standard logic program transformation to remove redundant data structures and arguments in predicates and rename predicates to make clear their link to statements in the original source program.

cs.PL↗
arXiv2018

Precondition Inference via Partitioning of Initial States

Precondition inference is a non-trivial task with several applications in program analysis and verification. We present a novel iterative method for automatically deriving sufficient preconditions for safety and unsafety of programs which introduces a new dimension of modularity. Each iteration maintains over-approximations of the set of \emph{safe} and \emph{unsafe} \emph{initial} states. Then we repeatedly use the current abstractions to partition the program's \emph{initial} states into those known to be safe, known to be unsafe and unknown, and construct a revised program focusing on those initial states that are not yet known to be safe or unsafe. An experimental evaluation of the method on a set of software verification benchmarks shows that it can solve problems which are not solvable using previous methods.

cs.LO↗
arXiv2018

An iterative approach to precondition inference using constrained Horn clauses

We present a method for automatic inference of conditions on the initial states of a program that guarantee that the safety assertions in the program are not violated. Constrained Horn clauses (CHCs) are used to model the program and assertions in a uniform way, and we use standard abstract interpretations to derive an over-approximation of the set of unsafe initial states. The precondition then is the constraint corresponding to the complement of that set, under-approximating the set of safe initial states. This idea of complementation is not new, but previous attempts to exploit it have suffered from the loss of precision. Here we develop an iterative specialisation algorithm to give more precise, and in some cases optimal safety conditions. The algorithm combines existing transformations, namely constraint specialisation, partial evaluation and a trace elimination transformation. The last two of these transformations perform polyvariant specialisation, leading to disjunctive constraints which improve precision. The algorithm is implemented and tested on a benchmark suite of programs from the literature in precondition inference and software verification competitions.

cs.LO↗
arXiv2018

Tree dimension in verification of constrained Horn clauses

In this paper, we show how the notion of tree dimension can be used in the verification of constrained Horn clauses (CHCs). The dimension of a tree is a numerical measure of its branching complexity and the concept here applies to Horn clause derivation trees. Derivation trees of dimension zero correspond to derivations using linear CHCs, while trees of higher dimension arise from derivations using non-linear CHCs. We show how to instrument CHCs predicates with an extra argument for the dimension, allowing a CHC verifier to reason about bounds on the dimension of derivations. Given a set of CHCs $P$, we define a transformation of $P$ yielding a dimension bounded set of CHCs $P^{\leq{k}}$. The set of derivations for $P^{\leq{k}}$ consists of the derivations for $P$ that have dimension at most $k$. We also show how to construct a set of clauses denoted $P^{>{k}}$ whose derivations have dimension exceeding $k$. We then present algorithms using these constructions to decompose a CHC verification problem. One variation of this decomposition considers derivations of successively increasing dimension. The paper includes descriptions of implementations and experimental results. Under consideration for publication in Theory and Practice of Logic Programming (TPLP).

cs.LO↗
arXiv2017

Optimised determinisation and completion of finite tree automata

Determinisation and completion of finite tree automata are important operations with applications in program analysis and verification. However, the complexity of the classical procedures for determinisation and completion is high. They are not practical procedures for manipulating tree automata beyond very small ones. In this paper we develop an algorithm for determinisation and completion of finite tree automata, whose worst-case complexity remains unchanged, but which performs far better than existing algorithms in practice. The critical aspect of the algorithm is that the transitions of the determinised (and possibly completed) automaton are generated in a potentially very compact form called product form, which can reduce the size of the representation dramatically. Furthermore, the representation can often be used directly when manipulating the determinised automaton. The paper contains an experimental evaluation of the algorithm on a large set of tree automata examples.

cs.FL↗
arXiv2016

Solving non-linear Horn clauses using a linear Horn clause solver

In this paper we show that checking satisfiability of a set of non-linear Horn clauses (also called a non-linear Horn clause program) can be achieved using a solver for linear Horn clauses. We achieve this by interleaving a program transformation with a satisfiability checker for linear Horn clauses (also called a solver for linear Horn clauses). The program transformation is based on the notion of tree dimension, which we apply to a set of non-linear clauses, yielding a set whose derivation trees have bounded dimension. Such a set of clauses can be linearised. The main algorithm then proceeds by applying the linearisation transformation and solver for linear Horn clauses to a sequence of sets of clauses with successively increasing dimension bound. The approach is then further developed by using a solution of clauses of lower dimension to (partially) linearise clauses of higher dimension. We constructed a prototype implementation of this approach and performed some experiments on a set of verification problems, which shows some promise.

cs.PL↗
arXiv2016

Interpolant Tree Automata and their Application in Horn Clause Verification

This paper investigates the combination of abstract interpretation over the domain of convex polyhedra with interpolant tree automata, in an abstraction-refinement scheme for Horn clause verification. These techniques have been previously applied separately, but are combined in a new way in this paper. The role of an interpolant tree automaton is to provide a generalisation of a spurious counterexample during refinement, capturing a possibly infinite set of spurious counterexample traces. In our approach these traces are then eliminated using a transformation of the Horn clauses. We compare this approach with two other methods; one of them uses interpolant tree automata in an algorithm for trace abstraction and refinement, while the other uses abstract interpretation over the domain of convex polyhedra without the generalisation step. Evaluation of the results of experiments on a number of Horn clause verification problems indicates that the combination of interpolant tree automaton with abstract interpretation gives some increase in the power of the verification tool, while sometimes incurring a performance overhead.

cs.LO↗
arXiv2016

ENTRA: Whole-Systems Energy Transparency

Promoting energy efficiency to a first class system design goal is an important research challenge. Although more energy-efficient hardware can be designed, it is software that controls the hardware; for a given system the potential for energy savings is likely to be much greater at the higher levels of abstraction in the system stack. Thus the greatest savings are expected from energy-aware software development, which is the vision of the EU ENTRA project. This article presents the concept of energy transparency as a foundation for energy-aware software development. We show how energy modelling of hardware is combined with static analysis to allow the programmer to understand the energy consumption of a program without executing it, thus enabling exploration of the design space taking energy into consideration. The paper concludes by summarising the current and future challenges identified in the ENTRA project.

cs.AR↗
arXiv2015

Decomposition by tree dimension in Horn clause verification

In this paper we investigate the use of the concept of tree dimension in Horn clause analysis and verification. The dimension of a tree is a measure of its non-linearity - for example a list of any length has dimension zero while a complete binary tree has dimension equal to its height. We apply this concept to trees corresponding to Horn clause derivations. A given set of Horn clauses P can be transformed into a new set of clauses P= k can be obtained from P whose derivation trees have dimension at least k + 1. In order to prove some property of all derivations of P, we systematically apply these transformations, for various values of k, to decompose the proof into separate proofs for P= k (which could be executed in parallel). We show some preliminary results indicating that decomposition by tree dimension is a potentially useful proof technique. We also investigate the use of existing automatic proof tools to prove some interesting properties about dimension(s) of feasible derivation trees of a given program.

cs.LO↗
arXiv2015

Solving non-linear Horn clauses using a linear solver

Developing an efficient non-linear Horn clause solver is a challenging task since the solver has to reason about the tree structures rather than the linear ones as in a linear solver. In this paper we propose an incremental approach to solving a set of non-linear Horn clauses using a linear Horn clause solver. We achieve this by interleaving a program transformation and a linear solver. The program transformation is based on the notion of tree dimension, which we apply to trees corresponding to Horn clause derivations. The dimension of a tree is a measure of its non-linearity -- for example a linear tree (whose nodes have at most one child) has dimension zero while a complete binary tree has dimension equal to its height. A given set of Horn clauses $P$ can be transformed into a new set of clauses $P^k$ (whose derivation trees are the subset of $P$'s derivation trees with dimension at most $k$). We start by generating $P^k$ with $k=0$, which is linear by definition, then pass it to a linear solver. If $P^k$ has a solution $M$, and is a solution to $P$ then $P$ has a solution $M$. If $M$ is not a solution of $P$, we plugged $M$ to $P^{(k+1)}$ which again becomes linear and pass it to the solver and continue successively for increasing value of $k$ until we find a solution to $P$ or resources are exhausted. Experiment on some Horn clause verification benchmarks indicates that this is a promising approach for solving a set of non-linear Horn clauses using a linear solver. It indicates that many times a solution obtained for some under-approximation $P^k$ of $P$ becomes a solution for $P$ for a fairly small value of $k$.

cs.LO↗
arXiv2014

Convex polyhedral abstractions, specialisation and property-based predicate splitting in Horn clause verification

We present an approach to constrained Horn clause (CHC) verification combining three techniques: abstract interpretation over a domain of convex polyhedra, specialisation of the constraints in CHCs using abstract interpretation of query-answer transformed clauses, and refinement by splitting predicates. The purpose of the work is to investigate how analysis and transformation tools developed for constraint logic programs (CLP) can be applied to the Horn clause verification problem. Abstract interpretation over convex polyhedra is capable of deriving sophisticated invariants and when used in conjunction with specialisation for propagating constraints it can frequently solve challenging verification problems. This is a contribution in itself, but refinement is needed when it fails, and the question of how to refine convex polyhedral analyses has not been studied much. We present a refinement technique based on interpolants derived from a counterexample trace; these are used to drive a property-based specialisation that splits predicates, leading in turn to more precise convex polyhedral analyses. The process of specialisation, analysis and splitting can be repeated, in a manner similar to the CEGAR and iterative specialisation approaches.

cs.LO↗
arXiv2014

Analysis and Transformation Tools for Constrained Horn Clause Verification

Several techniques and tools have been developed for verification of properties expressed as Horn clauses with constraints over a background theory (CHC). Current CHC verification tools implement intricate algorithms and are often limited to certain subclasses of CHC problems. Our aim in this work is to investigate the use of a combination of off-the-shelf techniques from the literature in analysis and transformation of Constraint Logic Programs (CLPs) to solve challenging CHC verification problems. We find that many problems can be solved using a combination of tools based on well-known techniques from abstract interpretation, semantics-preserving transformations, program specialisation and query-answer transformations. This gives insights into the design of automatic, more general CHC verification tools based on a library of components.

cs.PL↗