## Computation and specification models. A comparative study (2002)

Venue: | Department of Computer Science at University of Aarhus |

Citations: | 4 - 2 self |

### BibTeX

@INPROCEEDINGS{Börger02computationand,

author = {Egon Börger},

title = {Computation and specification models. A comparative study},

booktitle = {Department of Computer Science at University of Aarhus},

year = {2002},

pages = {107--130}

}

### OpenURL

### Abstract

For each of the principal current models of computation and of highlevel system design, we present a uniform set of transparent easily understandable descriptions, which are faithful to the basic intuitions and concepts of the investigated systems. Our main goal is to provide a mathematical basis for the technical comparison of established models of computation which can contribute to rationalize the scientific evaluation of different system specification approaches in the literature, clarifying in detail their advantages and disadvantages. As a side effect we obtain a powerful yet simple new conceptual framework for teaching the fundamentals of computation theory. 1

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Citation Context ...ream processing FSMs (stream processing components communicating among each other via input/output ports) by ASM state transformations of individual components. 4.1.3 Timed Automata In timed automata =-=[5]-=- letter input comes at a real-valued occurrence time which is used in the transitions where clocks record the time difference of the current input with respect to the previous input: time∆ = occurrenc... |

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Citation Context ... of inference rule applications. Most of these systems are not conceived to serve general-purpose specifications but are tailored to specific goals, the way Plotkin’s Structural Operational Semantics =-=[35]-=- or Kahn’s Natural Semantics or Mosses’ Action Semantics [45] are tailored for dealing with the semantics of programming languages. Numerous of these approaches are driven by structural patterns where... |

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Citation Context ...peaking sets of ASMs whose runs are defined by appropriately constrained partial orders to reflect the intended causal dependencies between steps of different machines. The definition can be found in =-=[39]-=- and in [26, Ch.6]. 5.1 Executable High-Level Design Languages We discuss here two major executable high-level design languages of the 90’ies. We relate their characteristic semantical features to ASM... |

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Citation Context ...ation theory. 1 Introduction The presentation of this work in the Action Semantics workshop started from Peter Mosses’ question to compare Action Notation (AN) [45] and Abstract State Machines (ASMs) =-=[26]-=-. Answering that question naturally led to a broader investigation, namely a comparative analysis of current specification and computation systems in terms of ASMs. In this paper we assume the reader ... |

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Citation Context ... . . . seq pn 19s5.2 State-based Specification Languages For sequential state-based specification languages we discuss three representative systems: VDM [33] (denotational), Z [57] (axiomatic), and B =-=[1]-=- (pseudocode). As representative distributed state-based modeling systems we relate Petri nets [47] to asynchronous ASMs. 5.2.1 VDM, Z, B These three high-level design languages share the notion of co... |

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Citation Context ... for teaching the fundamentals of computation theory. 1 Introduction The presentation of this work in the Action Semantics workshop started from Peter Mosses’ question to compare Action Notation (AN) =-=[45]-=- and Abstract State Machines (ASMs) [26]. Answering that question naturally led to a broader investigation, namely a comparative analysis of current specification and computation systems in terms of A... |

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Citation Context ...of Z specifications, their before-after expressions define the entire system dynamics. In B as in the ASM method, the formulation of the system dynamics—in B by operations (in event-based B by events =-=[2, 3, 4]-=-), in ASMs by rules—is separated from the formulation of the static state invariants 20sand of the dynamic run constraints, which express desired system properties one has to prove to hold through eve... |

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Citation Context ...iate to the specific purpose. Thus they ‘are’ particular ASMs. In fact for design or analysis purposes numerous virtual machines have been explicitly modeled as ASMs, e.g. the Warren Abstract Machine =-=[22]-=- and 21sits extensions [8, 23, 10, 9, 7], the Transputer [18], the RISC machine DLX [20], the Java Virtual Machine [52], the Neural Net (abstract data flow) Machine [25], the UPnP architecture [36]), ... |

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Citation Context ...theory. 3 UML Diagrams for System Dynamics For the modeling purpose, we use a generalization of Finite State Machines (FSMs) to a class of Abstract State Machines (ASMs) which have been introduced in =-=[15]-=- under the name of control state ASMs and are tailored to UML diagram visualizable machines. A control state ASM is an ASM whose rules are all of the following form: if ctl state = i then if cond1 the... |

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Citation Context ...de := next(candidates(currnode)) Delete(next(candidates(currnode)), currnode) We show now that by pure data refinements Backtrack can be turned into the backtracking engine for the core of ISO Prolog =-=[21]-=-, of IBM’s constraint logic programming language CLP(R) [23], of the functional programming language Babel [19], and also for context free and for attribute grammars [42]. 4.2.2 Logic Programming Engi... |

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Citation Context .... In fact for design or analysis purposes numerous virtual machines have been explicitly modeled as ASMs, e.g. the Warren Abstract Machine [22] and 21sits extensions [8, 23, 10, 9, 7], the Transputer =-=[18]-=-, the RISC machine DLX [20], the Java Virtual Machine [52], the Neural Net (abstract data flow) Machine [25], the UPnP architecture [36]), etc. 5.3 Logic Based Modeling Systems There is a myriad of lo... |

48 |
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Citation Context ...ose n ∈ N, choose p1, . . . , pn ∈ P roc p1 seq . . . seq pn 19s5.2 State-based Specification Languages For sequential state-based specification languages we discuss three representative systems: VDM =-=[33]-=- (denotational), Z [57] (axiomatic), and B [1] (pseudocode). As representative distributed state-based modeling systems we relate Petri nets [47] to asynchronous ASMs. 5.2.1 VDM, Z, B These three high... |

41 | An ASM semantics for UML Activity Diagrams
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Citation Context ...ly the conditions are supposed or guaranteed to be disjoint to avoid conflicting updates which would stop the ASM computation. Control state ASMs represent a normal form for UML activity diagrams (see=-=[17]-=-) from where they inherit the graphical representation of control states by circles or by (possibly named) directed arcs, to visually distinguish the control-passing role of control states from that o... |

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Citation Context ...ch-Turing thesis [38] led to an arguably most general notion of virtual machine which became the mathematical basis of the broadspectrum high-level ASM method for practical system design and analysis =-=[16]-=-. The differences in origin and goal explain also the major technical differences in the realization of AN and ASMs. Actions in AN categorize what in ASMs comes as abstract, a priori unclassified func... |

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28 | Composition and submachine concepts for sequential ASMs
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Citation Context ...rsion trees (with terminal yield except for the root variable), see [42]. 4.3 Structured Programming In this section we model standard structured programming constructs by natural classes of ASMs. In =-=[24]-=- two operators seq and iterate have been defined to compose ASMs sequentially and iteratively, capturing these two notions in a black-box view which fits the synchronous parallelism of ASMs, hiding in... |

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Citation Context ...rbo ASMs. A black-box submachine concept for value returning turbo ASMs has been defined in [24] which abstractly models the standard imperative calling mechanism. Triggered by the question raised in =-=[44]-=-: ‘If algorithms are machines, then which machine is the mergesort?’, the definition has been applied in [13] for simultaneous calls of multiple submachines, to seamlessly integrate functional descrip... |

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Citation Context ...lysis purposes numerous virtual machines have been explicitly modeled as ASMs, e.g. the Warren Abstract Machine [22] and 21sits extensions [8, 23, 10, 9, 7], the Transputer [18], the RISC machine DLX =-=[20]-=-, the Java Virtual Machine [52], the Neural Net (abstract data flow) Machine [25], the UPnP architecture [36]), etc. 5.3 Logic Based Modeling Systems There is a myriad of logic-based and algebraic spe... |

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Citation Context ...se between competing language development requirements, corresponding to views of the designer, the implementer and the programmer. Gurevich’s foundational concern to sharpen the Church-Turing thesis =-=[38]-=- led to an arguably most general notion of virtual machine which became the mathematical basis of the broadspectrum high-level ASM method for practical system design and analysis [16]. The differences... |

18 | Encoding Abstract State Machines in PVS - Gargantini, Riccobene - 2000 |

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17 |
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Citation Context ...ristic semantical features to ASMs, without mentioning further the important executability aspect which clearly influenced the choice of the language constructs. The languages are UNITY [28] and COLD =-=[32]-=-. 5.1.1 UNITY Unity computations are sequences of state transitions where each step comprises the simultaneous execution of multiple conditional variable assignments, including quantified array variab... |

16 | Verification of Compiler Correctness for the WAM - Pusch - 1996 |

15 | R.: CLAM Specification for Provably Correct Compilation of CLP(R
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Citation Context ...node)), currnode) We show now that by pure data refinements Backtrack can be turned into the backtracking engine for the core of ISO Prolog [21], of IBM’s constraint logic programming language CLP(R) =-=[23]-=-, of the functional programming language Babel [19], and also for context free and for attribute grammars [42]. 4.2.2 Logic Programming Engine We data refine here Backtrack to the backtracking engine ... |

14 | W.: The WAM case study: Verifying compiler correctness for Prolog with KIV - Schellhorn, Ahrendt - 1998 |

13 |
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Citation Context ...languages we discuss three representative systems: VDM [33] (denotational), Z [57] (axiomatic), and B [1] (pseudocode). As representative distributed state-based modeling systems we relate Petri nets =-=[47]-=- to asynchronous ASMs. 5.2.1 VDM, Z, B These three high-level design languages share the notion of computation as sequence of state transitions given by a before-after relation, where states are forme... |

12 | Correctness proof for the WAM with types
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Citation Context ...e. Thus they ‘are’ particular ASMs. In fact for design or analysis purposes numerous virtual machines have been explicitly modeled as ASMs, e.g. the Warren Abstract Machine [22] and 21sits extensions =-=[8, 23, 10, 9, 7]-=-, the Transputer [18], the RISC machine DLX [20], the Java Virtual Machine [52], the Neural Net (abstract data flow) Machine [25], the UPnP architecture [36]), etc. 5.3 Logic Based Modeling Systems Th... |

12 | M.: A Model for Mathematical Analysis of Functional Logic Programs and their Implementations. In
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Citation Context ...inements Backtrack can be turned into the backtracking engine for the core of ISO Prolog [21], of IBM’s constraint logic programming language CLP(R) [23], of the functional programming language Babel =-=[19]-=-, and also for context free and for attribute grammars [42]. 4.2.2 Logic Programming Engine We data refine here Backtrack to the backtracking engine for Prolog by instantiating the function alternativ... |

12 | High-level executable specification of the universal plug and play architecture
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Citation Context ...ne [22] and 21sits extensions [8, 23, 10, 9, 7], the Transputer [18], the RISC machine DLX [20], the Java Virtual Machine [52], the Neural Net (abstract data flow) Machine [25], the UPnP architecture =-=[36]-=-), etc. 5.3 Logic Based Modeling Systems There is a myriad of logic-based and algebraic specification and ‘declarative programming’ languages and calculi, like Prolog and its numerous variants, VDM, Z... |

11 | Zimmerman,w.: ASM-based mechanized verification of compiler back-ends - Dol, Gaul, et al. - 1998 |

10 |
Specification and Design of a Transmission Protocol by Successive Refinements Using B
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Citation Context ...of Z specifications, their before-after expressions define the entire system dynamics. In B as in the ASM method, the formulation of the system dynamics—in B by operations (in event-based B by events =-=[2, 3, 4]-=-), in ASMs by rules—is separated from the formulation of the static state invariants 20sand of the dynamic run constraints, which express desired system properties one has to prove to hold through eve... |

10 | E.: Specification and correctness proof of a WAM extension with abstract type constraints
- Beierle, Börger
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Citation Context ...e. Thus they ‘are’ particular ASMs. In fact for design or analysis purposes numerous virtual machines have been explicitly modeled as ASMs, e.g. the Warren Abstract Machine [22] and 21sits extensions =-=[8, 23, 10, 9, 7]-=-, the Transputer [18], the RISC machine DLX [20], the Java Virtual Machine [52], the Neural Net (abstract data flow) Machine [25], the UPnP architecture [36]), etc. 5.3 Logic Based Modeling Systems Th... |

9 | E.: Refinement of a typed WAM extension by polymorphic order-sorted types
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Citation Context ...e. Thus they ‘are’ particular ASMs. In fact for design or analysis purposes numerous virtual machines have been explicitly modeled as ASMs, e.g. the Warren Abstract Machine [22] and 21sits extensions =-=[8, 23, 10, 9, 7]-=-, the Transputer [18], the RISC machine DLX [20], the Java Virtual Machine [52], the Neural Net (abstract data flow) Machine [25], the UPnP architecture [36]), etc. 5.3 Logic Based Modeling Systems Th... |

9 |
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Citation Context ...ctly models the standard imperative calling mechanism. Triggered by the question raised in [44]: ‘If algorithms are machines, then which machine is the mergesort?’, the definition has been applied in =-=[13]-=- for simultaneous calls of multiple submachines, to seamlessly integrate functional description and programming techniques into ASMs. We illustrate this by a natural model for widely used forms of rec... |

9 | Verifikation abstrakter Zustandsmaschinen - Schellhorn - 1999 |

8 | Grammar formalisms viewed as evolving algebras
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Citation Context ...ne for the core of ISO Prolog [21], of IBM’s constraint logic programming language CLP(R) [23], of the functional programming language Babel [19], and also for context free and for attribute grammars =-=[42]-=-. 4.2.2 Logic Programming Engine We data refine here Backtrack to the backtracking engine for Prolog by instantiating the function alternatives to the function procdef(stm, pgm). This is a Prolog spec... |

8 |
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Citation Context ...n rule, j). 6sMealyAsms appear for example as components of co-design FSMs where rules are needed to compute arbitrary combinational (external and instantaneous) functions. Co-design FSMs are used in =-=[43]-=- for high-level architecture design and specification and for a precise comparison of current models of computation. Other examples of MealyAsms will be shown below. If one prefers to write FSM progra... |

7 | Generating an action notation environment from Montages descriptions
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Citation Context ..., compilers, etc., whereas ASMs support a general-purpose method which covers all system design and analysis aspects. In fact ASMs have been specialized to provide an executable semantics for AN, see =-=[6]-=- which contains also further details on tailoring ASMs to fit the AN framework. In the rest of this paper we use ASMs as a framework for a comparative analysis of other specification and computation s... |

7 |
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Citation Context ...x := t and parallel composition are derived). Differently from Z, which due to the purely axiomatic character of Z descriptions has intrinsic problems to turn specifications into executable code (see =-=[40]-=-), VDM and B are geared to obtain software modules from abstract specifications via refinements which are tailored to the proof rules used for proving that the refined operations satisfy ‘unchanged’ p... |

6 | A Formal Representation of Abstract State Machines Using PVS. Veri x - Dold - 1998 |

5 | A neural abstract machine
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Citation Context ...g. the Warren Abstract Machine [22] and 21sits extensions [8, 23, 10, 9, 7], the Transputer [18], the RISC machine DLX [20], the Java Virtual Machine [52], the Neural Net (abstract data flow) Machine =-=[25]-=-, the UPnP architecture [36]), etc. 5.3 Logic Based Modeling Systems There is a myriad of logic-based and algebraic specification and ‘declarative programming’ languages and calculi, like Prolog and i... |

5 |
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Citation Context ...out := b, j) in, out usually range over letters a, b, but one may also have words or other value types and also sets or sequences of input or output lines (ports), like in networks of finite automata =-=[27]-=-. The subclass of Moore automata is characterized by the same form of rules but with skip instead of the output assignment. This give rise to the generalization to Mealy/Moore ASMs defined in [15], a ... |

5 |
Syntax and Semantics of Graphs
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Citation Context ...n in: StreamProcessingFsm(P refix, T ransition) = choose pref ∈ P refix(ctl state, in) choose (c, o) ∈ T ransition(ctl state, pref) ctl state := c out := concatenate(o, out) in := delete(pref, in) In =-=[41]-=- these machines are used to enrich the classical networks of stream processing FSMs (stream processing components communicating among each other via input/output ports) by ASM state transformations of... |

4 |
Complexity, Logic (English translation of Berechenbarkeit, Komplexität, Logik , volume 128
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Citation Context ...ame underlying Scott’s definitional suggestions for automata theory [51]. In this section we suppose the reader to know the basic concepts of computation theory (see any textbook on the subject, e.g. =-=[14]-=-). 4.1 Automata We model here classical automata concepts, computationally universal ones as well as restricted machines. 4.1.1 Finite State Machines The standard FSMs, also known as Mealy automata, a... |

4 |
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Citation Context ...rom data refining the 1-tape Turing memory and the related operations and functions. Register machines are a data refined instance of k-tape Turing machines ([14, Ch.AI1]). 9sScott [51] and Eilenberg =-=[31]-=- instead of read/write operations on words stored in a tape provide data processing for arbitrary data, residing in abstract memory, by arbitrarily complex global mem-transforming functions. Eilenberg... |

3 |
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Citation Context |

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Citation Context ...of Z specifications, their before-after expressions define the entire system dynamics. In B as in the ASM method, the formulation of the system dynamics—in B by operations (in event-based B by events =-=[2, 3, 4]-=-), in ASMs by rules—is separated from the formulation of the static state invariants 20sand of the dynamic run constraints, which express desired system properties one has to prove to hold through eve... |