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Maximal causality analysis
 in: Conference on Application of Concurrency to System Design (ACSD
, 2005
"... Perfectly synchronous systems immediately react to the inputs of their environment, which may lead to socalled causality cycles between actions and their trigger conditions. Algorithms to analyze the consistency of such cycles usually extend data types by an additional value to explicitly indicate ..."
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Cited by 19 (18 self)
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Perfectly synchronous systems immediately react to the inputs of their environment, which may lead to socalled causality cycles between actions and their trigger conditions. Algorithms to analyze the consistency of such cycles usually extend data types by an additional value to explicitly indicate unknown values. In particular, Boolean functions are thereby extended to ternary functions. However, a Boolean function usually has several ternary extensions, and the result of the causality analysis depends on the chosen ternary extension. In this paper, we show that there always is a maximal ternary extension that allows one to solve as many causality problems as possible. Moreover, we elaborate the relationship to hazard elimination in hardware circuits, and finally show how the maximal ternary extension of a Boolean function can be efficiently computed by means of binary decision diagrams.
Improving Constructiveness in Code Generators
, 2005
"... Perfectly synchronous systems immediately react to the inputs of their environment. These instantaneous reactions may result in socalled causality cycles between the actions of a system and their preconditions. Programs with causality cycles may or may not have consistent and unambiguous behaviors. ..."
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Cited by 11 (10 self)
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Perfectly synchronous systems immediately react to the inputs of their environment. These instantaneous reactions may result in socalled causality cycles between the actions of a system and their preconditions. Programs with causality cycles may or may not have consistent and unambiguous behaviors. For this reason, compilers have to perform a causality analysis before code generation. In this paper, we analyze the impact of different code generation schemes on causality analysis and propose translations that yield different degrees of causality. To this end, we first translate the program to an equation system as an intermediate representation, which may alternatively be viewed as a hardware circuit. The second step then analyzes the equation system as known from ternary simulation of hardware circuits with combinational feedback loops. In particular, we consider alternative ways to obtain logically equivalent equation systems that show, however, different results in causality analysis.
Timing Analysis of Combinational Circuits in Intuitionistic Propositional Logic
 Formal Methods in System Design
, 1999
"... Classical logic has so far been the logic of choice in formal hardware verification. This paper proposes the application of intuitionistic logic to the timing analysis of digital circuits. The intuitionistic setting serves two purposes. The modeltheoretic properties are exploited to handle the s ..."
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Cited by 7 (1 self)
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Classical logic has so far been the logic of choice in formal hardware verification. This paper proposes the application of intuitionistic logic to the timing analysis of digital circuits. The intuitionistic setting serves two purposes. The modeltheoretic properties are exploited to handle the secondorder nature of bounded delays in a purely propositional setting without need to introduce explicit time and temporal operators. The proof theoretic properties are exploited to extract quantitative timing information and to reintroduce explicit time in a convenient and systematic way. We present a natural Kripkestyle semantics for intuitionistic propositional logic, as a special case of a Kripke constraint model for Propositional Lax Logic [15], in which validity is validity up to stabilisation, and implication oe comes out as "boundedly gives rise to." We show that this semantics is equivalently characterised by a notion of realisability with stabilisation bounds as realisers...
Characterising Combinational Timing Analyses in Intuitionistic Modal Logic
, 2000
"... The paper presents a new logical specification language, called Propositional Stabilisation Theory (PST), to capture the stabilisation behaviour of combinational inputoutput systems. PST is an intuitionistic propositional modal logic interpreted over sets of waveforms. The language is more economic ..."
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Cited by 6 (4 self)
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The paper presents a new logical specification language, called Propositional Stabilisation Theory (PST), to capture the stabilisation behaviour of combinational inputoutput systems. PST is an intuitionistic propositional modal logic interpreted over sets of waveforms. The language is more economic than conventional specification formalisms such as timed Boolean functions, temporal logic, or predicate logic in that it separates function from time and only introduces as much syntax as is necessary to deal with stabilisation behaviour. It is a purely propositional system but has secondorder expressiveness. One and the same Boolean function can be represented in various ways as a PST formula, giving rise to different timing models which associate different stabilisation delays with different parts of the functionality and adjust the granularity of the datadependency of delays within wide margins. We show how several standard timing analyses can be characterised as algorithms computing c...
Timing Analysis of Cyclic Combinational Circuits
"... The accepted wisdom is that combinational circuits must have acyclic (i.e., loopfree or feedforward) topologies. And yet simple examples suggest that this need not be so. In previous work, we advocated the design of cyclic combinational circuits (i.e., circuits with loops or feedback paths). We pr ..."
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Cited by 3 (1 self)
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The accepted wisdom is that combinational circuits must have acyclic (i.e., loopfree or feedforward) topologies. And yet simple examples suggest that this need not be so. In previous work, we advocated the design of cyclic combinational circuits (i.e., circuits with loops or feedback paths). We proposed a methodology for analyzing and synthesizing such circuits, with an emphasis on the optimization of area.
Algorithmic Aspects of Cyclic Combinational Circuit Synthesis
"... Abstract — Digital circuits are called combinational if they are memoryless: they have outputs that depend only on the current values of the inputs. Combinational circuits are generally thought of as acyclic (i.e., feedforward) structures. And yet, cyclic circuits can be combinational. Cycles somet ..."
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Abstract — Digital circuits are called combinational if they are memoryless: they have outputs that depend only on the current values of the inputs. Combinational circuits are generally thought of as acyclic (i.e., feedforward) structures. And yet, cyclic circuits can be combinational. Cycles sometimes occur in designs synthesized from highlevel descriptions, as well as in busbased designs [16]. Feedback in such cases is carefully contrived, typically occurring when functional units are connected in a cyclic topology. Although the premise of cycles in combinational circuits has been accepted, and analysis techniques have been proposed [7], no one has attempted the synthesis of circuits with feedback at the logic level. We have argued the case for a paradigm shift in combinational circuit design [10]. We should no longer think of combinational logic as acyclic in theory or in practice, since most combinational circuits are best designed with cycles. We have proposed a general methodology for the synthesis of multilevel networks with cyclic topologies and incorporated it in a general logic synthesis environment. In trials, benchmark circuits were optimized significantly, with improvements of up to 30% in the area. In this paper, we discuss algorithmic aspects of cyclic circuit design. We formulate a symbolic framework for analysis based on a divideandconquer strategy. Unlike previous approaches, our method does not require ternaryvalued simulation. Our analysis for combinationality is tightly coupled with the synthesis phase, in which we assemble a combinational network from smaller combinational components. We discuss the underpinnings of the heuristic search methods and present examples as well as synthesis results for benchmark circuits.
SLAP 2005 Preliminary Version Improving Constructiveness in Code Generators
"... Perfectly synchronous systems immediately react to the inputs of their environment. These instantaneous reactions may result in socalled causality cycles between the actions of a system and their preconditions. Programs with causality cycles may or may not have consistent and unambiguous behaviors ..."
Abstract
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Perfectly synchronous systems immediately react to the inputs of their environment. These instantaneous reactions may result in socalled causality cycles between the actions of a system and their preconditions. Programs with causality cycles may or may not have consistent and unambiguous behaviors. For this reason, compilers have to perform a causality analysis before code generation. In this paper, we analyze the impact of different code generation schemes on causality analysis and propose translations that yield different degrees of causality. To this end, we first translate the program to an equation system as an intermediate representation, which may alternatively be viewed as a hardware circuit. The second step then analyzes the equation system as known from ternary simulation of hardware circuits with combinational feedback loops. In particular, we consider alternative ways to obtain logically equivalent equation systems that show, however, different results in causality analysis. Key words: synchronous programming languages, programming language semantics, ternary simulation, causality analysis 1
Abstraction and Constraints: Two Sides of the Same Coin
, 1997
"... ion and Constraints: Two Sides of the Same Coin M.Walton November 1997 University of Sheffield Department of Computer Science Technical Report CS9718 Abstraction and Constraints: Two Sides of the Same Coin M. Walton PhD Supervisor: M.V.H. Fairtlough Abstract This report presents a highlev ..."
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ion and Constraints: Two Sides of the Same Coin M.Walton November 1997 University of Sheffield Department of Computer Science Technical Report CS9718 Abstraction and Constraints: Two Sides of the Same Coin M. Walton PhD Supervisor: M.V.H. Fairtlough Abstract This report presents a highlevel survey of some approaches to abstraction and the wide range of fields in which their applications may be found. Whilst there is much to be found in the literature about either abstraction or constraints, very little is to be found about them both, or the relationship between them. We examine the role of a novel intuitionistic modal logic (called Lax Logic) in capturing the dual notions of abstraction and constraints, and a particular notion of refinement. As a specific application of Lax Logic, we look at its use as an abstraction framework for the paradigm of Constraint Logic Programming. This provides a novel declarative and operational semantics for CLP which offers a clean separation...