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Relations and Refinement in Circuit Design
 Proc. BCS FACS Workshop on Refinement, Workshops in Computing
, 1991
"... A language of relations and combining forms is presented in which to describe both the behaviour of circuits and the specifications which they must meet. We illustrate a design method that starts by selecting representations for the values on which a circuit operates, and derive the circuit from the ..."
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A language of relations and combining forms is presented in which to describe both the behaviour of circuits and the specifications which they must meet. We illustrate a design method that starts by selecting representations for the values on which a circuit operates, and derive the circuit from these representations by a process of refinement entirely within the language. Formal methods have always been used in circuit design. It would be unthinkable to attempt to design combinational circuits without using Boolean algebra. This means that circuit designers, unlike programmers, already use mathematical tools as a matter of course. It also means that we have a good basis on which to build higher level formal design methods. Encouraged by these observations, we have been investigating the application of formal program development techniques to circuit design. We view circuit design as the transformation of a program describing the required behaviour into an equivalent program that is s...
Using Recursive Types to Reason about Hardware in Higher Order Logic
, 1988
"... : The expressive power of higher order logic makes it possible to define a wide variety of data types within the logic and to prove theorems that state the properties of these types concisely and abstractly. This paper describes how such defined data types can be used to support formal reasoning in ..."
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Cited by 19 (1 self)
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: The expressive power of higher order logic makes it possible to define a wide variety of data types within the logic and to prove theorems that state the properties of these types concisely and abstractly. This paper describes how such defined data types can be used to support formal reasoning in higher order logic about the behaviour of hardware designs. First printed: May 1988 Reprinted with revisions: April 1990 An earlier version of this paper appears in: The Fusion of Hardware Design and Verification, ed. G.J. Milne (NorthHolland, 1988), pp. 2750. Contents Introduction 5 1 Hardware Verification using Higher Order Logic 5 1.1 Notation : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 5 1.2 Specifying Hardware Behaviour : : : : : : : : : : : : : : : : : : 6 1.3 Specifying Hardware Structure : : : : : : : : : : : : : : : : : : 7 1.4 Formulating Correctness : : : : : : : : : : : : : : : : : : : : : : 8 2 Recursive Types in Higher Order Logic 8 2.1 Type Definit...
Annotated Reasoning
 Annals of Mathematics and Artificial Intelligence (AMAI). Special Issue on Strategies in Automated Deduction
, 2000
"... Proof Search According to [12], abstract proof search is a process by which, starting from a representation of a problem at a socalled ground level, we construct a new and simpler representation at a socalled abstract level and use it to solve the original problem. That is, we abstract the given ..."
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Proof Search According to [12], abstract proof search is a process by which, starting from a representation of a problem at a socalled ground level, we construct a new and simpler representation at a socalled abstract level and use it to solve the original problem. That is, we abstract the given goal, prove its abstracted version and then use the information about the resulting abstract proof as an outline to construct the proof at the ground level. Dierent techniques to abstract from details have been studied in the literature. The problem is to nd out which details should be abstracted away. On one hand, if we abstract too much information then we often obtain abstract solutions that cannot be transferred to the ground level. Then, planning at the abstract level is even more dicult than planning at the ground level because the abstraction removes necessary control information, or we obtain only little information from the abstract proof how to guide the proof at the ground leve...
A Transformational Approach to Formal Digital System Design
, 1993
"... syntax for design annotations : : : : : : : : : : : : : : : : : 45 4.3 Semantic algebras for design annotations : : : : : : : : : : : : : : : : 46 4.4 Semantic algebras, continued : : : : : : : : : : : : : : : : : : : : : : : 47 4.5 Valuation functions for design annotations : : : : : : : : : : : : ..."
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Cited by 12 (0 self)
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syntax for design annotations : : : : : : : : : : : : : : : : : 45 4.3 Semantic algebras for design annotations : : : : : : : : : : : : : : : : 46 4.4 Semantic algebras, continued : : : : : : : : : : : : : : : : : : : : : : : 47 4.5 Valuation functions for design annotations : : : : : : : : : : : : : : : 48 4.6 Devices : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 50 5.1 Constant dummy in the basic library : : : : : : : : : : : : : : : : : : 58 5.2 Interconnection devices in the basic library : : : : : : : : : : : : : : : 58 5.3 Devices in the comp library : : : : : : : : : : : : : : : : : : : : : : : 59 5.4 Timing analysis of the design in session box 7 : : : : : : : : : : : : : 66 5.5 Scheduling the design in session box 7 : : : : : : : : : : : : : : : : : : 67 5.6 The design after session box 8 : : : : : : : : : : : : : : : : : : : : : : 68 5.7 The design after session box 15 : : : : : : : : : : : : : : : : : : : : : 74 5.8 The design after session box 16 : : :...
Toward the Rigorous Use of Diagrams in Reasoning about Hardware
 IULG Preprint Series
, 1993
"... We propose that the concept of "formal methods" be expansive enough to include a rigorous, integrated use of diagrams for automated reasoning tasks. Applications to hardware design provide an especially rich domain to explore visually oriented extensions of traditional logic. This domain h ..."
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We propose that the concept of "formal methods" be expansive enough to include a rigorous, integrated use of diagrams for automated reasoning tasks. Applications to hardware design provide an especially rich domain to explore visually oriented extensions of traditional logic. This domain has an established methodology embracing the use of diagrams; it promises to light the way toward modernizing the foundations of formal logic. In this paper we examine some of the issues exposed when one attempts to develop a rigorous basis for heterogeneous and visually oriented reasoning. . Toward the Rigorous Use of Diagrams in Reasoning about Hardware Steven D. Johnson , Jon Barwise, and Gerard T. Allwein. Johnson's research supported, in part, by the National Science Foundation under grants numbered MIP8921842 and MIP9208745. 2 Author's name Introduction The logician's conventional notion of proof has grown increasingly anachronistic through the twentieth century as computing capabilities...
Exploiting the Potential of Diagrams in Guiding Hardware Reasoning
 in Logical Reasoning with Diagrams, G. Allwein and
, 1996
"... Formal methods promises designers increased assurance in and understanding of their designs. Assurance is gained via proof; understanding is gained via the construction of proof. Researchers have developed powerful proof techniques; they have not focused sufficiently on creating tools to support rea ..."
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Cited by 4 (0 self)
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Formal methods promises designers increased assurance in and understanding of their designs. Assurance is gained via proof; understanding is gained via the construction of proof. Researchers have developed powerful proof techniques; they have not focused sufficiently on creating tools to support reasoning. As a result, formal methods fails to attain its full potential. We argue that by formalizing the notations provided by diagrammatic representations, we can build tools that provide support for both proof and reasoning, thereby making formal methods more widely applicable by designers. 1 Introduction Formal methods offer much more to computer science than just "proofs of correctness" for programs and digital circuits, however. Many of the problems in software and hardware design are due to imprecision, ambiguity, incompleteness, misunderstanding, and just plain mistakes in the statement of toplevel requirements, in the description of intermediate designs, or in the specification of ...
A Logical Formalization of Hardware Design Diagrams
, 1994
"... Diagrams have been left as an informal tool in hardware reasoning, thus rendering them unacceptable representations within formal reasoning systems. We demonstrate some advantages of formally supporting diagrams in hardware verification systems via a simple example and provide a logical formalizatio ..."
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Diagrams have been left as an informal tool in hardware reasoning, thus rendering them unacceptable representations within formal reasoning systems. We demonstrate some advantages of formally supporting diagrams in hardware verification systems via a simple example and provide a logical formalization of hardware diagrams upon which we are constructing a verification tool. 1 Introduction The increased use of formal methods for verifying hardware specifications has generated a wealth of research into the formal models and representations of hardware that best facilitate the verification task. Most such models are based on combinations of temporal and higherorder logic which, while effective, do not necessarily reflect the models used during the design process. The hardware design process involves the use of a collection of diagrammatic forms, such as circuit diagrams and timing diagrams, which depict certain characteristics of hardware components more naturally than purely sentential r...
Automatic Data Path Abstraction for Verification of Large Scale Designs
 in Proc. of ICCD’98
, 1998
"... ..."
Structure and Behaviour in Hardware Verification
 Higher Order Logic Theorem Proving and its applications, 6th International Workshop, HUG ’93, Vancouver, B.C. Canada, number 780 in Lecture
, 1993
"... In this paper we review how hardware has been described in the formal hardware verification community. Recent developments in hardware description are evaluated against the background of the use of hardware description languages, and also in relation to programming languages. The notions of structur ..."
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In this paper we review how hardware has been described in the formal hardware verification community. Recent developments in hardware description are evaluated against the background of the use of hardware description languages, and also in relation to programming languages. The notions of structure and behaviour are crucial to this discussion. 1 Introduction Hardware has long been described using hardware description languages (hdls). More recently, in the field of hardware verification logicbased notations have been used. In this paper we explore how the relationship between the structure and behaviour of circuits has been perceived over time in the formal verification field. The structure of this paper is as follows: we give our view of hdls and simulation prior to the advent of formal methods, then we comment on formal logic methods used to describe and reason about hardware. Connections with conventional programming languages are also explored. Hardware Description Languages an...
Verification in Higher Order Logic of Mutual Exclusion Algorithm
 IN HIGHER ORDER LOGIC THEOREM PROVING AND ITS APPLICATIONS
, 1993
"... In this work a mutual exclusion algorithm is modeled using Transition Assertions. The main feature of a mutual exclusion algorithm is to prevent simultaneous access of a shared resource by two or more systems. The specification of the algorithm is a collection of transition assertions with each tr ..."
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In this work a mutual exclusion algorithm is modeled using Transition Assertions. The main feature of a mutual exclusion algorithm is to prevent simultaneous access of a shared resource by two or more systems. The specification of the algorithm is a collection of transition assertions with each transition assertion containing a precondition and postcondition. The Transition Assertions model is formalized in higher order logic and the HOL mechanized theorem prover is used to show that the Transition Assertions model complies with the mutual exclusion requirement.