First-Order Models for Configuration Analysis

Our world teems with networked devices. Their configuration exerts an ever-expanding influence on our daily lives. Yet correctly configuring systems, networks, and access-control policies is notoriously difficult, even for trained professionals. Automated static analysis techniques provide a way to both verify a configuration\u27s correctness and explore its implications. One such approach is scenario-finding: showing concrete scenarios that illustrate potential (mis-)behavior. Scenarios even have a benefit to users without technical expertise, as concrete examples can both trigger and improve users\u27 intuition about their system. This thesis describes a concerted research effort toward improving scenario-finding tools for configuration analysis. We developed Margrave, a scenario-finding tool with special features designed for security policies and configurations. Margrave is not tied to any one specific policy language; rather, it provides an intermediate input language as expressive as first-order logic. This flexibility allows Margrave to reason about many different types of policy. We show Margrave in action on Cisco IOS, a common language for configuring firewalls, demonstrating that scenario-finding with Margrave is useful for debugging and validating real-world configurations. This thesis also presents a theorem showing that, for a restricted subclass of first-order logic, if a sentence is satisfiable then there must exist a satisfying scenario no larger than a computable bound. For such sentences scenario-finding is complete: one can be certain that no scenarios are missed by the analysis, provided that one checks up to the computed bound. We demonstrate that many common configurations fall into this subclass and give algorithmic tests for both sentence membership and counting. We have implemented both in Margrave. Aluminum is a tool that eliminates superfluous information in scenarios and allows users\u27 goals to guide which scenarios are displayed. We quantitatively show that our methods of scenario-reduction and exploration are effective and quite efficient in practice. Our work on Aluminum is making its way into other scenario-finding tools. Finally, we describe FlowLog, a language for network programming that we created with analysis in mind. We show that FlowLog can express many common network programs, yet demonstrate that automated analysis and bug-finding for FlowLog are both feasible as well as complete

Reasoning About Strategies: On the Model-Checking Problem

In open systems verification, to formally check for reliability, one needs an appropriate formalism to model the interaction between agents and express the correctness of the system no matter how the environment behaves. An important contribution in this context is given by modal logics for strategic ability, in the setting of multi-agent games, such as ATL, ATL\star, and the like. Recently, Chatterjee, Henzinger, and Piterman introduced Strategy Logic, which we denote here by CHP-SL, with the aim of getting a powerful framework for reasoning explicitly about strategies. CHP-SL is obtained by using first-order quantifications over strategies and has been investigated in the very specific setting of two-agents turned-based games, where a non-elementary model-checking algorithm has been provided. While CHP-SL is a very expressive logic, we claim that it does not fully capture the strategic aspects of multi-agent systems. In this paper, we introduce and study a more general strategy logic, denoted SL, for reasoning about strategies in multi-agent concurrent games. We prove that SL includes CHP-SL, while maintaining a decidable model-checking problem. In particular, the algorithm we propose is computationally not harder than the best one known for CHP-SL. Moreover, we prove that such a problem for SL is NonElementarySpace-hard. This negative result has spurred us to investigate here syntactic fragments of SL, strictly subsuming ATL\star, with the hope of obtaining an elementary model-checking problem. Among the others, we study the sublogics SL[NG], SL[BG], and SL[1G]. They encompass formulas in a special prenex normal form having, respectively, nested temporal goals, Boolean combinations of goals and, a single goal at a time. About these logics, we prove that the model-checking problem for SL[1G] is 2ExpTime-complete, thus not harder than the one for ATL\star

Variables

Variables is a project at the intersection of the philosophies of language and logic. Frege, in the Begriffsschrift, crystalized the modern notion of formal logic through the first fully successful characterization of the behaviour of quantifiers. In Variables, I suggest that the logical tradition we have inherited from Frege is importantly flawed, and that Frege's move from treating quantifiers as noun phrases bearing word-world connection to sentential operators in the guise of second-order predicates leaves us both philosophically and technically wanting

Reconstructing Z3 Proofs With KeY

KeY dient zur formalen Verifikation spezifizierter Eigenschaften von Java-Programmen.Dafür werden aus der formalen Spezifikation sowie dem Programm-Code Beweisverpflichtungen generiert. Diese werden dann Schritt für Schritt in eine Menge von Formeln der Prädikatenlogik erster Stufe überführt. Da diese allerdings unentscheidbar ist, ist es eine große Herausforderung, einen Beweis für diese Formelmenge zu finden. Moderne SMT-Solver, wie zum Beispiel Z3, sind genau auf diesen Anwendungszweck hin optimiert. Daher ist schon lange in KeY die Möglichkeit eingebaut, (Teil-)Probleme für SMT-Solver zu übersetzen. Das Ergebnis bei diesem Vorgehen ist ein partieller Beweis in KeY, der von (möglicherweise mehreren) SMT-Antworten komplettiert wird. Da Z3 aber auch Beweise für seine Antworten liefern kann, gibt es hier Verbesserungspotential: In dieser Thesis wird eine Technik zum Nachspielen der Z3 Beweise in KeY vorgestellt, sodass man als Ergebnis einen geschlossenen Beweis in KeY erhält und die SMT-Antworten verworfen werden können. Herausforderungen sowohl systematischer als auch technischer Natur werden identifiziert and Lösungen dafür vogestellt. Schließlich wird auch eine prototypische Implementierung der Technik zum Nachspielen der Beweise zur Verfügung gestellt. Im Evaluations-Teil der Arbeit wird die Leistungsfähigkeit dieser Implementierung sowie die zukünfigen Möglichkeiten erörtert

Verification-based software-fault detection

Software is used in many safety- and security-critical systems. Software development is, however, an error-prone task. In this work new techniques for the detection of software faults (or software "bugs") are described which are based on a formal deductive verification technology. The described techniques take advantage of information obtained during verification and combine verification technology with deductive fault detection and test generation in a very unified way

Disproving in First-Order Logic with Definitions, Arithmetic and Finite Domains

This thesis explores several methods which enable a first-order reasoner to conclude satisfiability of a formula modulo an arithmetic theory. The most general method requires restricting certain quantifiers to range over finite sets; such assumptions are common in the software verification setting. In addition, the use of first-order reasoning allows for an implicit representation of those finite sets, which can avoid scalability problems that affect other quantified reasoning methods. These new techniques form a useful complement to existing methods that are primarily aimed at proving validity. The Superposition calculus for hierarchic theory combinations provides a basis for reasoning modulo theories in a first-order setting. The recent account of ‘weak abstraction’ and related improvements make an mplementation of the calculus practical. Also, for several logical theories of interest Superposition is an effective decision procedure for the quantifier free fragment. The first contribution is an implementation of that calculus (Beagle), including an optimized implementation of Cooper’s algorithm for quantifier elimination in the theory of linear integer arithmetic. This includes a novel means of extracting values for quantified variables in satisfiable integer problems. Beagle won an efficiency award at CADE Automated theorem prover System Competition (CASC)-J7, and won the arithmetic non-theorem category at CASC-25. This implementation is the start point for solving the ‘disproving with theories’ problem. Some hypotheses can be disproved by showing that, together with axioms the hypothesis is unsatisfiable. Often this is relative to other axioms that enrich a base theory by defining new functions. In that case, the disproof is contingent on the satisfiability of the enrichment. Satisfiability in this context is undecidable. Instead, general characterizations of definition formulas, which do not alter the satisfiability status of the main axioms, are given. These general criteria apply to recursive definitions, definitions over lists, and to arrays. This allows proving some non-theorems which are otherwise intractable, and justifies similar disproofs of non-linear arithmetic formulas. When the hypothesis is contingently true, disproof requires proving existence of a model. If the Superposition calculus saturates a clause set, then a model exists, but only when the clause set satisfies a completeness criterion. This requires each instance of an uninterpreted, theory-sorted term to have a definition in terms of theory symbols. The second contribution is a procedure that creates such definitions, given that a subset of quantifiers range over finite sets. Definitions are produced in a counter-example driven way via a sequence of over and under approximations to the clause set. Two descriptions of the method are given: the first uses the component solver modularly, but has an inefficient counter-example heuristic. The second is more general, correcting many of the inefficiencies of the first, yet it requires tracking clauses through a proof. This latter method is shown to apply also to lists and to problems with unbounded quantifiers. Together, these tools give new ways for applying successful first-order reasoning methods to problems involving interpreted theories

Verification-based Software-fault Detection

Software is used in many safety- and security-critical systems. Software development is, however, an error-prone task. In this dissertation new techniques for the detection of software faults (or software "bugs") are described which are based on a formal deductive verification technology. The described techniques take advantage of information obtained during verification and combine verification technology with deductive fault detection and test generation in a very unified way

An SMT-based verification framework for software systems handling arrays

Recent advances in the areas of automated reasoning and first-order theorem proving paved the way to the developing of effective tools for the rigorous formal analysis of computer systems. Nowadays many formal verification frameworks are built over highly engineered tools (SMT-solvers) implementing decision procedures for quantifier- free fragments of theories of interest for (dis)proving properties of software or hardware products. The goal of this thesis is to go beyond the quantifier-free case and enable sound and effective solutions for the analysis of software systems requiring the usage of quantifiers. This is the case, for example, of software systems handling array variables, since meaningful properties about arrays (e.g., "the array is sorted") can be expressed only by exploiting quantification. The first contribution of this thesis is the definition of a new Lazy Abstraction with Interpolants framework in which arrays can be handled in a natural manner. We identify a fragment of the theory of arrays admitting quantifier-free interpolation and provide an effective quantifier-free interpolation algorithm. The combination of this result with an important preprocessing technique allows the generation of the required quantified formulae. Second, we prove that accelerations, i.e., transitive closures, of an interesting class of relations over arrays are definable in the theory of arrays via Exists-Forall-first order formulae. We further show that the theoretical importance of this result has a practical relevance: Once the (problematic) nested quantifiers are suitably handled, acceleration offers a precise (not over-approximated) alternative to abstraction solutions. Third, we present new decision procedures for quantified fragments of the theories of arrays. Our decision procedures are fully declarative, parametric in the theories describing the structure of the indexes and the elements of the arrays and orthogonal with respect to known results. Fourth, by leveraging our new results on acceleration and decision procedures, we show that the problem of checking the safety of an important class of programs with arrays is fully decidable. The thesis presents along with theoretical results practical engineering strategies for the effective implementation of a framework combining the aforementioned results: The declarative nature of our contributions allows for the definition of an integrated framework able to effectively check the safety of programs handling array variables while overcoming the individual limitations of the presented techniques