Avner Landver

Establishing PCI compliance using formal verification: a case study

Proceedings International Phoenix Conference on Computers and Communications

This paper presents a case study in the practical application of formal verification. Specificall... more

Panel: Assertion-Based Verification -What's the Big Deal?

2006 IEEE International High Level Design Validation and Test Workshop, 2006

Abstract Summary form only given. Assertion based validation of hardware and software systems has... more Abstract Summary form only given. Assertion based validation of hardware and software systems has been in use in the industry for a long time. In the software languages such as C++ or Java, there are special assert constructs that are used to specify a Boolean condition. These conditions express what the programmers think ought to hold, at specific points in their programs. Violations of such assertions provide clues about the program state at those points during execution and hence indicate the existence of bugs. In hardware design ...

Baire numbers, uncountable Cohen sets and perfect-set forcing

Journal of Symbolic Logic, 1992

The Baire number of the real line (see 1.1(c)) has uncountable cofinality [Mi]. This number is eq... more The Baire number of the real line (see 1.1(c)) has uncountable cofinality [Mi]. This number is equal to the Baire number of the space 2ω and also to the Baire number (1.1(d)) of every countable partial order. Our research is motivated by the following open question (1.13) (see also [BPS] and [Mi]): can the cofinality of nκ, the Baire number of the space (2κ)κ (1.1(b)), be less than or equal to κ? This question is nontrivial when κ is regular and 2κ = κ (1.3). A. Miller proved that the answer is “no” if κ is strongly inaccessible (see [Mi] and 1.11). Assuming CH, is equal to the Baire number of the Stone space of ℘(ω)/Fin.In §1 we discuss , the Baire number of the space (2λ)κ. If κ is regular, then , and using 1.3 and 1.5, we may rule out the easy cases and restrict ourselves to cases where κ is regular with 2<κ = κ, and κ ≤ λ 2κ. If λ > κ, then it is consistent to have cof()=κ ([Mi] and 1.7). We do not know whether is consistent (1.9). Next, the cardinal number eκ is defined (...

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Finite combinations of Baire numbers

Israel Journal of Mathematics, 1993

Let κ be a regular cardinal. Consider the Baire numbers of the spaces (2 θ) κ for various θ ≥ κ. ... more Let κ be a regular cardinal. Consider the Baire numbers of the spaces (2 θ) κ for various θ ≥ κ. Let l be the number of such different Baire numbers. Models of set theory with l = 1 or l = 2 are known and it is also known that l is finite. We show here that if κ > ω, then l could be any given finite number.

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The ForSpec Temporal Logic: A New Temporal Property-Specification Language

Lecture Notes in Computer Science, 2002

In this paper we describe the ForSpec Temporal Logic (FTL), the new temporal property-specificati... more In this paper we describe the ForSpec Temporal Logic (FTL), the new temporal property-specification logic of ForSpec, Intel's new formal specification language. The key features of FTL are as follows: it is a linear temporal logic, based on Pnueli's LTL, it is based on a rich set of logical and arithmetical operations on bit vectors to describe state properties, it enables the user to define temporal connectives over time windows, it enables the user to define regular events, which are regular sequences of Boolean events, and then relate such events via special connectives, it enables the user to express properties about the past, and it includes constructs that enable the user to model multiple clock and reset signals, which is useful in the verification of hardware design.

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Formal Verification of a Processor's Bus Interface Unit

This report describes formal verification of a processor's Bus Interface Unit (hereafter is ... more This report describes formal verification of a processor's Bus Interface Unit (hereafter is called BIU). The methodology employed in this project consisted of first formally verifying the individual blocks, and then the entire control logic of the design. In all, 73 control logic bugs were detected, some of which would have been difficult to find using simulation. Formal verification was the most productive component in the logic verification of the BIU. This project provides an example of the successful application of formal verification, as embedded in RuleBase, a tool that was designed in IBM Haifa Research Laboratory, to a full scale industrial design.

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Coverage-directed test generation using symbolic techniques

Lecture Notes in Computer Science, 1996

In practice, verification by simulation is carded out by running a relatively small sub-set of se... more In practice, verification by simulation is carded out by running a relatively small sub-set of selected tests, since the test space is typically very large. One of the critical aspects of verification by simulation is the definition of appropriate measurable criteria for the quality of the test set in terms of ...

Remark on the Failure of Martin's Axiom

Eprint Arxiv Math 9207205, Jul 31, 1992

Let m be the least cardinal θ such that MA θ fails. The only known model for "m is singular" was ... more Let m be the least cardinal θ such that MA θ fails. The only known model for "m is singular" was constructed by Kunen [K1]. In Kunen's model cof (m) = ω 1 . It is unknown whether "ω 1 < cof (m) < m" is consistent. The purpose of this paper is to present a proof of Kunen's result and to identify the difficulties of generalizing this result to an arbitrary uncountable cofinality. The following material is based on [K1]. We would like to thank K. Kunen and S. Shelah [S] for their input. §0 Definitions and some facts. For undefined terminology consult [K]. Let θ be a fixed singular cardinal with uncountable cofinality. Let κ = cof (θ), and fix {θ α : α < κ} an increasing sequence of cardinals converging to θ with θ 0 > κ. For a disjoint pair (A, B) we define the partial order S(A, B) = {f : θ → ω : |f | < ℵ 0 and (∀ξ, η ∈ dom(f )) (a ξ -f (ξ))∩(b η -f (η)) = ∅}. S(A, B) is partially ordered by inclusion. It is well known that if (A, B) is locally split, then S(A, B) is c.c.c., and therefore, if in addition MA θ holds, then (A, B) can be split (to split (A, B) use the set c = {a ξf (ξ) : f ∈ G, ξ ∈ dom(f )} Where G is a sufficiently generic filter on S(A, B)).

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RuleBase: Model checking at IBM

Computer Aided …, 1997

RuleBase is a symbolic model checking tool, developed by the IBM Haifa Research Laboratory with t... more

Tightness in products of fans and psuedo-fans

Topology and its Applications, 1995

Abstract Give κ the discrete topology and ω + 1 the order topology. The κ-fan Fκ is the quotient ... more Abstract Give κ the discrete topology and ω + 1 the order topology. The κ-fan Fκ is the quotient space obtained by identifying the nonisolated points of κ × (ω + 1) to a point ∞. We investigate the tightness of products of the form Fκ × Fλ, where λ ⩽ κ. Some of our results are t(Fκ × Fλ) ⩽ λω, t + (F ℵ ω × F ℵ ω ) ⩽ ℵ ω , and a new connection between the tightness of Fκ × Fλ and the failure of ⩽ κ-cwH in first countable

Singular σ-dense trees

The Journal of Symbolic Logic, 1992

Let be the least cardinal θ such that MAθ fails, (i.e. MA) implies that is regular. Models for re... more Let be the least cardinal θ such that MAθ fails, (i.e. MA) implies that is regular. Models for regular with are easy to get (see [Ku1]). Fremlin and Miller proved that cof() > ω [Fr, 41C(d)]. The question of whether it is consistent that be singular was solved, in the affirmative, by Kunen [Ku1]. Kunen used a (θ, θ) strong gap in (ω)/Fin, whose splitting partial order is c.c.c. He showed that if cof(θ) = ω1, and P is a c.c.c. partial order of cardinality < θ that may destroy the strong gap, then there exists another c.c.c. partial order Q, which does not destroy the strong gap, and such that ⊩Q “P is not c.c.c”. One then gets…

On-the-fly model checking of RCTL formulas

Lecture Notes in Computer Science, 1998

The specification language _RCTL, an extension of CTL, is defined by adding the power of regular ... more The specification language _RCTL, an extension of CTL, is defined by adding the power of regular expressions to CTL. In addition to being a more expressive and natural hardware specification language than CTL, a large family of RCTL formulas can be verified on-the-fly (during symbolic teachability analysis). On-the-fly model checking, as a powerful verification paradigm, is especially efficient when the specification is false and extremely efficient when the computation needed to get to a failing state is short. It is suitable for the inherently gradual design process since it detects a multitude of bugs at the early verification stages, and paves the way towards finding the more complex errors as the design matures. It is shown that for every erroneous finite computation, there is an RCTL formula that detects it and can be verified on-the-fly. On-thefly verification of RCTL formulas has moved model checking in IBM into a different class of designs inaccessible by prior techniques.

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RuleBase

Proceedings of the 33rd annual conference on Design automation conference - DAC '96, 1996

RuleBase is a formal verification tool, developed by the IBM Haifa Research Laboratory. It is the... more RuleBase is a formal verification tool, developed by the IBM Haifa Research Laboratory. It is the result of three years of experience in practical formal verification of hardware which, we believe, has been a key factor in bringing the tool to its current level of maturity. We present the tool, including several unique features, and summa- rize our usage experience.

Reflection and weakly collectionwise Hausdorff spaces

Proceedings of the American Mathematical Society, 1994

We show that 0(0) implies that there is a first countable < 6collectionwise Hausdorff space that ... more We show that 0(0) implies that there is a first countable < 6collectionwise Hausdorff space that is not weakly (9-collectionwise Hausdorff. We also show that in the model obtained by Levy collapsing a weakly compact (supercompact) cardinal to a>2, first countable ¡»^-collectionwise Hausdorff spaces are weakly ^-collectionwise Hausdorff (weakly collectionwise Hausdorff). In the last section we show that assuming E% , a certain 0-family of integer-valued functions exists and that in the model obtained by Levy collapsing a supercompact cardinal to u>i. these families do not exist.

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The ForSpec Temporal Logic: A New Temporal Property-Specification Language

by Andreas Tiemeyer, Eli Singerman, Avner Landver, and Sela Mador-Haim

Lecture Notes in Computer Science, 2002

In this paper we describe the ForSpec Temporal Logic (FTL), the new temporal property-specificati... more In this paper we describe the ForSpec Temporal Logic (FTL), the new temporal property-specification logic of ForSpec, Intel's new formal specification language. The key features of FTL are as follows: it is a linear temporal logic, based on Pnueli's LTL, it is based on a rich set of logical and arithmetical operations on bit vectors to describe state properties, it enables the user to define temporal connectives over time windows, it enables the user to define regular events, which are regular sequences of Boolean events, and then relate such events via special connectives, it enables the user to express properties about the past, and it includes constructs that enable the user to model multiple clock and reset signals, which is useful in the verification of hardware design. which is typically the hardware description language used by the designers). In designing a formal specification language one has to balance several competing needs:

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