Matteo Pradella

Operator Precedence Languages (OPL) have been recently identified as a suitable formalism for model checking recursive procedural programs, thanks to their ability of modeling the program stack. OPL requirements can be expressed in thePrecedence Oriented Temporal Logic(), which features modalities to reason on the natural matching between function calls and returns, exceptions, and other advanced programming constructs that previous approaches, such as Visibly Pushdown Languages, cannot model effectively. Existing approaches for model checking of have been designed following the explicit-state, automata-based approach, a feature that severely limits their scalability. In this paper, we give the first symbolic, SMT-based approach for model checking properties. While previous approaches construct the automaton for both the formula and the model of the program, we encode them into a (sequence of) SMT formulas. The search of a trace of the model witnessing a violation of the formula is then carried out by an SMT-solver, in a Bounded Model Checking fashion. We carried out an experimental evaluation, which shows the effectiveness of the proposed solution.

Operator Precedence Languages (OPL) have been recently identified as a suitable formalism for model checking recursive procedural programs, thanks to their ability of modeling the program stack. OPL requirements can be expressed in the Precedence Oriented Temporal Logic (POTL), which features modalities to reason on the natural matching between function calls and returns, exceptions, and other advanced programming constructs that previous approaches, such as Visibly Pushdown Languages, cannot model effectively. Existing approaches for model checking of POTL have been designed following the explicit-state, automata-based approach, a feature that severely limits their scalability. In this paper, we give the first symbolic, SMT-based approach for model checking POTL properties. While previous approaches construct the automaton for both the POTL formula and the model of the program, we encode them into a (sequence of) SMT formulas. The search of a trace of the model witnessing a violation of the formula is then carried out by an SMT-solver, in a Bounded Model Checking fashion. We carried out an experimental evaluation, which shows the effectiveness of the proposed solution.

A classic result in formal language theory is the equivalence among non-counting, or aperiodic, regular languages, and languages defined through star-free regular expressions, or first-order logic. Past attempts to extend this result beyond the realm of regular languages have met with difficulties: for instance it is known that star-free tree languages may violate the non-counting property and there are aperiodic tree languages that cannot be defined through first-order logic. We extend such classic equivalence results to a significant family of deterministic context-free languages, the operator-precedence languages (OPL), which strictly includes the widely investigated visibly pushdown, alias input-driven, family and other structured context-free languages. The OP model originated in the '60s for defining programming languages and is still used by high performance compilers; its rich algebraic properties have been investigated initially in connection with grammar learning and recently completed with further closure properties and with monadic second order logic definition. We introduce an extension of regular expressions, the OP-expressions (OPE) which define the OPLs and, under the star-free hypothesis, define first-order definable and non-counting OPLs. Then, we prove, through a fairly articulated grammar transformation, that aperiodic OPLs are first-order definable. Thus, the classic equivalence of star-freeness, aperiodicity, and first-order definability is established for the large and powerful class of OPLs. We argue that the same approach can be exploited to obtain analogous results for visibly pushdown languages too.

The problem of extending model checking from finite state machines to procedural programs has fostered much research toward the definition of temporal logics for reasoning on context-free structures. The most notable of such results are temporal logics on Nested Words, such as CaRet and NWTL. Recently, Precedence Oriented Temporal Logic (POTL) has been introduced to specify and prove properties of programs coded trough an Operator Precedence Language (OPL). POTL is complete w.r.t. the FO restriction of the MSO logic previously defined as a logic fully equivalent to OPL. POTL increases NWTL’s expressive power in a perfectly parallel way as OPLs are more powerful that nested words. In this article, we produce a model checker, named POMC, for OPL programs to prove properties expressed in POTL. To the best of our knowledge, POMC is the first implemented and openly available model checker for proving tree-structured properties of recursive procedural programs. We also report on the experimental evaluation we performed on POMC on a nontrivial benchmark.

Operator precedence languages (OPL) enjoy the local parsability property, which essentially means that a code fragment enclosed within a pair of markers -- playing the role of parentheses -- can be compiled with no knowledge of its external context. Such a property has been exploited to build parallel compilers for languages formalized as OPLs. It has been observed, however, that when the syntax trees of the sentences have a linear substructure, its parsing must necessarily proceed sequentially making it impossible to split such a subtree into chunks to be processed in parallel. Such an inconvenience is due to the fact that so far much literature on OPLs has assumed the hypothesis that equality precedence relation cannot be cyclic. This hypothesis was motivated by the need to keep the mathematical notation as simple as possible. We present an enriched version of operator precedence grammars, called cyclic, that allows to use a simplified version of regular expressions in the right hand sides of grammar's rules; for this class of operator precedence grammars the acyclicity hypothesis of the equality precedence relation is no more needed to guarantee the algebraic properties of the generated languages. The expressive power of the cyclic grammars is now fully equivalent to that of other formalisms defining OPLs such as operator precedence automata, monadic second order logic and operator precedence expressions. As a result cyclic operator precedence grammars now produce also unranked syntax trees and sentences with flat unbounded substructures that can be naturally partitioned into chunks suitable for parallel parsing.

The increasing use of Infrastructure as Code (IaC) in DevOps leads to benefits in speed and reliability of deployment operation, but extends to infrastructure challenges typical of software systems. IaC scripts can contain defects that result in security and reliability issues in the deployed infrastructure: techniques for detecting and preventing them are needed. We analyze and survey the current state of research in this respect by conducting a literature review on static analysis techniques for IaC. We describe analysis techniques, defect categories and platforms targeted by tools in the literature.