Formal Verification, Model Checking
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Experiments in Validating Formal Semantics for C
Experiments in validating formal semantics for C Sandrine Blazy ENSIIE and INRIA Rocquencourt [email protected] Abstract. This paper reports on the design of adequate on-machine formal semantics for a certified C compiler. This compiler is an optimiz- ing compiler, that targets critical embedded software. It is written and formally verified using the Coq proof assistant. The main structure of the compiler is very strongly conditioned by the choice of the languages of the compiler, and also by the kind of semantics of these languages. 1 Introduction C is still widely used in industry, especially for developing embedded software. The main reason is the control by the C programmer of all the resources that are required for program execution (e.g. memory layout, memory allocation) and that affect performance. C programs can therefore be very efficient, but the price to pay is a programming effort. For instance, using C pointer arithmetic may be required in order to compute the address of a memory cell. However, a consequence of this freedom given to the C programmer is the presence of run-time errors such as buffer overflows and dangling pointers. Such errors may be difficult to detect in programs, because of C type casts and more generally because the C type system is unsafe. Many static analysis tools attempt to detect such errors in order to ensure safety properties that may be ensured by more recent languages such as Java. For instance, CCured is a program transformation system that adds memory safety guarantees to C programs by verifying statically that memory errors cannot oc- cur and by inserting run-time checks where static verification is insufficient [1]. -
Model Checking
Lecture 1: Model Checking Edmund Clarke School of Computer Science Carnegie Mellon University 1 Cost of Software Errors June 2002 “Software bugs, or errors, are so prevalent and so detrimental that they cost the U.S. economy an estimated $59.5 billion annually, or about 0.6 percent of the gross domestic product … At the national level, over half of the costs are borne by software users and the remainder by software developers/vendors.” NIST Planning Report 02-3 The Economic Impacts of Inadequate Infrastructure for Software Testing 2 Cost of Software Errors “The study also found that, although all errors cannot be removed, more than a third of these costs, or an estimated $22.2 billion, could be eliminated by an improved testing infrastructure that enables earlier and more effective identification and removal of software defects.” 3 Model Checking • Developed independently by Clarke and Emerson and by Queille and Sifakis in early 1980’s. • Properties are written in propositional temporal logic. • Systems are modeled by finite state machines. • Verification procedure is an exhaustive search of the state space of the design. • Model checking complements testing/simulation. 4 Advantages of Model Checking • No proofs!!! • Fast (compared to other rigorous methods) • Diagnostic counterexamples • No problem with partial specifications / properties • Logics can easily express many concurrency properties 5 Model of computation Microwave Oven Example State-transition graph describes system evolving ~ Start ~ Close over time. ~ Heat st ~ Error Start ~ Start ~ Start ~ Close Close Close ~ Heat Heat ~ Heat Error ~ Error ~ Error Start Start Start Close Close Close ~ Heat ~ Heat Heat Error ~ Error ~ Error 6 Temporal Logic l The oven doesn’t heat up until the door is closed. -
Model Checking TLA Specifications
Model Checking TLA+ Specifications Yuan Yu1, Panagiotis Manolios2, and Leslie Lamport1 1 Compaq Systems Research Center {yuanyu,lamport}@pa.dec.com 2 Department of Computer Sciences, University of Texas at Austin [email protected] Abstract. TLA+ is a specification language for concurrent and reac- tive systems that combines the temporal logic TLA with full first-order logic and ZF set theory. TLC is a new model checker for debugging a TLA+ specification by checking invariance properties of a finite-state model of the specification. It accepts a subclass of TLA+ specifications that should include most descriptions of real system designs. It has been used by engineers to find errors in the cache coherence protocol for a new Compaq multiprocessor. We describe TLA+ specifications and their TLC models, how TLC works, and our experience using it. 1 Introduction Model checkers are usually judged by the size of system they can handle and the class of properties they can check [3,16,4]. The system is generally described in either a hardware-description language or a language tailored to the needs of the model checker. The criteria that inspired the model checker TLC are completely different. TLC checks specifications written in TLA+, a rich language with a well-defined semantics that was designed for expressiveness and ease of formal reasoning, not model checking. Two main goals led us to this approach: – The systems that interest us are too large and complicated to be completely verified by model checking; they may contain errors that can be found only by formal reasoning. We want to apply a model checker to finite-state models of the high-level design, both to catch simple design errors and to help us write a proof. -
Introduction to Model Checking and Temporal Logic¹
Formal Verification Lecture 1: Introduction to Model Checking and Temporal Logic¹ Jacques Fleuriot [email protected] ¹Acknowledgement: Adapted from original material by Paul Jackson, including some additions by Bob Atkey. I Describe formally a specification that we desire the model to satisfy I Check the model satisfies the specification I theorem proving (usually interactive but not necessarily) I Model checking Formal Verification (in a nutshell) I Create a formal model of some system of interest I Hardware I Communication protocol I Software, esp. concurrent software I Check the model satisfies the specification I theorem proving (usually interactive but not necessarily) I Model checking Formal Verification (in a nutshell) I Create a formal model of some system of interest I Hardware I Communication protocol I Software, esp. concurrent software I Describe formally a specification that we desire the model to satisfy Formal Verification (in a nutshell) I Create a formal model of some system of interest I Hardware I Communication protocol I Software, esp. concurrent software I Describe formally a specification that we desire the model to satisfy I Check the model satisfies the specification I theorem proving (usually interactive but not necessarily) I Model checking Introduction to Model Checking I Specifications as Formulas, Programs as Models I Programs are abstracted as Finite State Machines I Formulas are in Temporal Logic 1. For a fixed ϕ, is M j= ϕ true for all M? I Validity of ϕ I This can be done via proof in a theorem prover e.g. Isabelle. 2. For a fixed ϕ, is M j= ϕ true for some M? I Satisfiability 3. -
Model Checking and the Curse of Dimensionality
Model Checking and the Curse of Dimensionality Edmund M. Clarke School of Computer Science Carnegie Mellon University Turing's Quote on Program Verification . “How can one check a routine in the sense of making sure that it is right?” . “The programmer should make a number of definite assertions which can be checked individually, and from which the correctness of the whole program easily follows.” Quote by A. M. Turing on 24 June 1949 at the inaugural conference of the EDSAC computer at the Mathematical Laboratory, Cambridge. 3 Temporal Logic Model Checking . Model checking is an automatic verification technique for finite state concurrent systems. Developed independently by Clarke and Emerson and by Queille and Sifakis in early 1980’s. The assertions written as formulas in propositional temporal logic. (Pnueli 77) . Verification procedure is algorithmic rather than deductive in nature. 4 Main Disadvantage Curse of Dimensionality: “In view of all that we have said in the foregoing sections, the many obstacles we appear to have surmounted, what casts the pall over our victory celebration? It is the curse of dimensionality, a malediction that has plagued the scientist from the earliest days.” Richard E. Bellman. Adaptive Control Processes: A Guided Tour. Princeton University Press, 1961. Image courtesy Time Inc. 6 Photographer Alfred Eisenstaedt. Main Disadvantage (Cont.) Curse of Dimensionality: 0,0 0,1 1,0 1,1 2-bit counter n-bit counter has 2n states 7 Main Disadvantage (Cont.) 1 a 2 | b n states, m processes | 3 c 1,a nm states 2,a 1,b 3,a 2,b 1,c 3,b 2,c 3,c 8 Main Disadvantage (Cont.) Curse of Dimensionality: The number of states in a system grows exponentially with its dimensionality (i.e. -
PROGRAM VERIFICATION Robert S. Boyer and J
PROGRAM VERIFICATION Robert S. Boyer and J Strother Moore To Appear in the Journal of Automated Reasoning The research reported here was supported by National Science Foundation Grant MCS-8202943 and Office of Naval Research Contract N00014-81-K-0634. Institute for Computing Science and Computer Applications The University of Texas at Austin Austin, Texas 78712 1 Computer programs may be regarded as formal mathematical objects whose properties are subject to mathematical proof. Program verification is the use of formal, mathematical techniques to debug software and software specifications. 1. Code Verification How are the properties of computer programs proved? We discuss three approaches in this article: inductive invariants, functional semantics, and explicit semantics. Because the first approach has received by far the most attention, it has produced the most impressive results to date. However, the field is now moving away from the inductive invariant approach. 1.1. Inductive Assertions The so-called Floyd-Hoare inductive assertion method of program verification [25, 33] has its roots in the classic Goldstine and von Neumann reports [53] and handles the usual kind of programming language, of which FORTRAN is perhaps the best example. In this style of verification, the specifier "annotates" certain points in the program with mathematical assertions that are supposed to describe relations that hold between the program variables and the initial input values each time "control" reaches the annotated point. Among these assertions are some that characterize acceptable input and the desired output. By exploring all possible paths from one assertion to the next and analyzing the effects of intervening program statements it is possible to reduce the correctness of the program to the problem of proving certain derived formulas called verification conditions. -
Formal Verification of Diagnosability Via Symbolic Model Checking
Formal Verification of Diagnosability via Symbolic Model Checking Alessandro Cimatti Charles Pecheur Roberto Cavada ITC-irst RIACS/NASA Ames Research Center ITC-irst Povo, Trento, Italy Moffett Field, CA, U.S.A. Povo, Trento, Italy mailto:[email protected] [email protected] [email protected] Abstract observed system. We propose a new, practical approach to the verification of diagnosability, making the following contribu• This paper addresses the formal verification of di• tions. First, we provide a formal characterization of diagnos• agnosis systems. We tackle the problem of diagnos• ability problem, using the idea of context, that explicitly takes ability: given a partially observable dynamic sys• into account the run-time conditions under which it should be tem, and a diagnosis system observing its evolution possible to acquire certain information. over time, we discuss how to verify (at design time) Second, we show that a diagnosability condition for a given if the diagnosis system will be able to infer (at run• plant is violated if and only if a critical pair can be found. A time) the required information on the hidden part of critical pair is a pair of executions that are indistinguishable the dynamic state. We tackle the problem by look• (i.e. share the same inputs and outputs), but hide conditions ing for pairs of scenarios that are observationally that should be distinguished (for instance, to prevent simple indistinguishable, but lead to situations that are re• failures to stay undetected and degenerate into catastrophic quired to be distinguished. We reduce the problem events). We define the coupled twin model of the plant, and to a model checking problem. -
Theorem Proving for Verification
Theorem Proving for Verification John Harrison Intel Corporation CAV 2008 Princeton 9th July 2008 0 Formal verification Formal verification: mathematically prove the correctness of a design with respect to a mathematical formal specification. Actual requirements 6 Formal specification 6 Design model 6 Actual system 1 Essentials of formal verification The basic steps in formal verification: Formally model the system • Formalize the specification • Prove that the model satisfies the spec • But what formalism should be used? 2 Some typical formalisms Propositional logic, a.k.a. Boolean algebra • Temporal logic (CTL, LTL etc.) • Quantifier-free combinations of first-order arithmetic theories • Full first-order logic • Higher-order logic or first-order logic with arithmetic or set theory • 3 Expressiveness vs. automation There is usually a roughly inverse relationship: The more expressive the formalism, the less the ‘proof’ is amenable to automation. For the simplest formalisms, the proof can be so highly automated that we may not even think of it as ‘theorem proving’ at all. The most expressive formalisms have a decision problem that is not decidable, or even semidecidable. 4 Logical syntax English Formal false ⊥ true ⊤ not p p ¬ p and q p q ∧ p or q p q ∨ p implies q p q ⇒ p iff q p q ⇔ for all x, p x. p ∀ there exists x such that p x. p ∃ 5 Propositional logic Formulas built up from atomic propositions (Boolean variables) and constants , using the propositional connectives , , , and ⊥ ⊤ ¬ ∧ ∨ ⇒ . ⇔ No quantifiers or internal structure to the atomic propositions. 6 Propositional logic Formulas built up from atomic propositions (Boolean variables) and constants , using the propositional connectives , , , and ⊥ ⊤ ¬ ∧ ∨ ⇒ . -
ACM 2007 Turing Award Edmund Clarke, Allen Emerson, and Joseph Sifakis Model Checking: Algorithmic Verification and Debugging
ACM 2007 Turing Award Edmund Clarke, Allen Emerson, and Joseph Sifakis Model Checking: Algorithmic Verification and Debugging ACM Turing Award Citation precisely describe what constitutes correct behavior. This In 1981, Edmund M. Clarke and E. Allen Emerson, work- makes it possible to contemplate mathematically establish- ing in the USA, and Joseph Sifakis working independently ing that the program behavior conforms to the correctness in France, authored seminal papers that founded what has specification. In most early work, this entailed constructing become the highly successful field of Model Checking. This a formal proof of correctness. In contradistinction, Model verification technology provides an algorithmic means of de- Checking avoids proofs. termining whether an abstract model|representing, for ex- ample, a hardware or software design|satisfies a formal Hoare-style verification was the prevailing mode of formal specification expressed as a temporal logic formula. More- verification going back from the late-1960s until the 1980s. over, if the property does not hold, the method identifies This classic and elegant approach entailed manual proof con- a counterexample execution that shows the source of the struction, using axioms and inference rules in a formal de- problem. ductive system, oriented toward sequential programs. Such proof construction was tedious, difficult, and required hu- The progression of Model Checking to the point where it man ingenuity. This field was a great academic success, can be successfully used for complex systems has required spawning work on compositional or modular proof systems, the development of sophisticated means of coping with what soundness of program proof systems, and their completeness; is known as the state explosion problem. -
Safety Standards and WCET Analysis Tools Daniel Kästner, Christian Ferdinand
Safety Standards and WCET Analysis Tools Daniel Kästner, Christian Ferdinand To cite this version: Daniel Kästner, Christian Ferdinand. Safety Standards and WCET Analysis Tools. Embedded Real Time Software and Systems (ERTS2012), Feb 2012, Toulouse, France. hal-02192406 HAL Id: hal-02192406 https://hal.archives-ouvertes.fr/hal-02192406 Submitted on 23 Jul 2019 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Safety Standards and WCET Analysis Tools Daniel Kastner¨ Christian Ferdinand AbsInt GmbH, Science Park 1, D-66123 Saarbrucken,¨ Germany http://www.absint.com Abstract of-the-art techniques for verifying software safety re- quirements have to be applied to make sure that an appli- In automotive, railway, avionics, automation, and cation is working properly. To do so lies in the responsi- healthcare industries more and more functionality is im- bility of the system designers. Ensuring software safety plemented by embedded software. A failure of safety- is one of the goals of safety standards like DO-178B, critical software may cause high costs or even endan- DO-178C, IEC-61508, ISO-26262, or EN-50128. They ger human beings. Also for applications which are not all require to identify functional and non-functional haz- highly safety-critical, a software failure may necessitate ards and to demonstrate that the software does not vio- expensive updates. -
Introduction to Model-Checking Theory and Practice
Introduction to Model-Checking Theory and Practice Beihang International Summer School 2018 Model Checking Linear Temporal Properties Model Checking “Model checking is the method by which a desired behavioral property of a reactive system is verified over a given system (the model) through exhaustive enumeration (explicit or implicit ) of all the states reachable by the system and the behaviors that traverse through them” Amir Pnueli (2000) Basic Properties • reachability (something is possible) • invariant (something is always true) the gate is closed when the train cross the road • safety (something bad never happen: ≡ ¬ 푅푒푎푐ℎ) • liveness (something good may eventually happen) every process will (eventually) gain access to the printer • Fairness (if it may happen ∞ often then it will happen) if messages cannot be lost ∞ often then I will received an ack Model-Checking • We have seen how to use a formal specification language to model the system (⇒ as a graph, but also as a language ℒ) • We have seen how to check basic properties on the reachability graph (and that SCC can be useful) • What if we want to check more general properties? User-Defined Properties • present before (we should see an 푎 before the first 푏) the latch must be locked before take-off • infinitely often (something will always happen, ≠ 퐴푙푤푎푦푠) the timer should always be triggered • leadsto (after every occurrence of 푎 there should be a 푏) there is an audible signal after the alarm is activated • … see example of specification patterns here [Dwyer] Model-Checking System + Requirements informal Description Description M of the of the 휙 behavior property operational denotational formalization verification Does 푀 ⊨ 휙 Does 푀 ≡ 퐺휙 yes / no / c. -
Model Checking Software in Cyberphysical Systems
Model Checking Software in Cyberphysical Systems Marjan Sirjani Ehsan Khamespanah Edward A. Lee School of IDT ECE Department Department of EECS Mälardalen University University of Tehran UC Berkeley Västerås, Sweden Tehran, Iran Berkeley, USA [email protected] [email protected] [email protected] Abstract—Model checking a software system is about verifying where software reads sensor data and issues commands to that the state trajectory of every execution of the software satisfies physical actuators, ignoring this relationship is more dangerous. formally specified properties. The set of possible executions is For CPS, verification is ultimately about assuring properties modeled as a transition system. Each “state” in the transition system represents an assignment of values to variables, and a state of the physical world not the software abstraction. This means trajectory (a path through the transition system) is a sequence that it is not sufficient to study the software alone. We need of such assignments. For cyberphysical systems (CPSs), however, to also study its interactions with its environment. we are more interested in the state of the physical system than Of course, there is nothing new about formally studying the values of the software variables. The value of model checking the interactions of software with its environment. In 1977, for the software therefore depends on the relationship between the state of the software and the state of the physical system. This example, Pnueli was developing temporal logics for reactive relationship can be complex because of the real-time nature of systems [1]. In 1985, Harel and Pnueli singled out reactive the physical plant, the sensors and actuators, and the software systems as being “particularly problematic when it comes to that is almost always concurrent and distributed.