Blieberger, J., and Lieger, R. Worst-case space and time complexity of recursive procedures. Real-Time Systems 11, 2 (1996), 115--144.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....independent of input size, i.e. are constants while the computation iterates or recurses. Whatever values of the primitive cost parameters are assumed, a second problem arises, and it is theoretically 3 challenging: optimizing the cost bound function to a closed form in terms of the input size [50, 10, 26, 41, 17, 7]. Although much progress has been made in this area, closed forms are known only for subclasses of functions. Thus, such optimization can not be automatically done for analyzing general programs. In systems, inputs are characterized indirectly using loop bounds or execution paths in programs, and ....

....appears in Section 2. Certain detailed comparisons have also been discussed while presenting our method. This section summarizes them, compares with analyses for loop bounds and execution paths in more detail, and concludes. Compared to work in algorithm analysis and program complexity analysis [26, 44, 53, 7], this work consistently pushes through symbolic primitive cost parameters, so it allows us to calculate actual cost bounds and validate the results with experimental measurements. There is also work on analyzing average case complexity [17] which has a di erent goal than worst case bounds. ....

J. Blieberger and R. Lieger. Worst-case space and time complexity of recursive procedures. Real-Time Systems, 11(2):115-144, 1996.

....at runtime with little effort. If one of them is violated the exception recursionMepth error is raised. If the compiler cannot prove the properties mentioned above, additional runtime checks become necessary to guarantee that all space and time requirements are met. Details can be found in [2]. 7 Implementing Mergesort A recursive implementation of Mergesort using our real time recursions is given in Figure 3. Function celng(x) is supposed to implement Ix] and ld(x) denotes the binary logarithm. Note that the programmer s task is extremely easy. All necessary proofs and checks can ....

....In this paper we have demonstrated how recursive procedures can be constrained in order to use them in real time applications without harm. We have set up conditions which easily can be checked at compile time. Thus our approach is wellsuited for real time applications. In our forth coming paper [2] we will give more ex amples of our approach. In addition, we develop a method how one can abstract from unnecessary details of the algorithm during estimating space and time properties, and we give prerequisites for real time programming languages which incorporate our approach. Finally we ....

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J. Biteberger and R. Lieger. Worst-case space and time complexity of recursive procedures. (to appear), 1994.

.... an upper bound of the WCET of RealTime Euclid programs is described in [SHH91] Although in the meantime it has been proved that more general loopstatements can be used in real time programming languages (cf. Bli94] and that recursion can be employed without harm in real time systems (cf. BL96, Bli00] the concept of schedulability analysis, which is also introduced in [HS91] is still very important for real time applications. One of the minor results of this paper is that goto statements can be used for implementing real time systems without prohibiting schedulability analysis, ....

....of time values. Time can be measured either by natural numbers (e.g. number of machine cycles) or by real numbers. Thus T is either equal to N 0 or to R 0 . # We ignore recursive procedures here. Solutions to the problem of WCET analysis of recursive real time procedures can be found in [BL95, BL96, Bli00] 8 J. BLIEBERGER We associate with each basic block B a number # B # T which accounts for the time used by the execution of B. We assume that each # B is invariable, i.e. the timing behavior of a basic block does not change if it is executed several times. This excludes e#ects of ....

[Article contains additional citation context not shown here]

Johann Blieberger and Roland Lieger, Worst-case space and time complexity of recursive procedures, Real-Time Systems 11 (1996), no. 2, 115--144. 1, 7, 28

....at runtime with little effort. If one of them is violated the exception recursion depth error is raised. If the compiler cannot prove the properties mentioned above, additional runtime checks become necessary to guarantee that all space and time requirements are met. Details can be found in [2]. 7 Implementing Mergesort A recursive implementation of Mergesort using our real time recursions is given in Figure 3. Function ceiling(x) is supposed to implement dxe and ld(x) denotes the binary logarithm. Note that the programmer s task is extremely easy. All necessary proofs and checks can ....

....In this paper we have demonstrated how recursive procedures can be constrained in order to use them in real time applications without harm. We have set up conditions which easily can be checked at compile time. Thus our approach is wellsuited for real time applications. In our forth coming paper [2] we will give more examples of our approach. In addition, we develop a method how one can abstract from unnecessary details of the algorithm during estimating space and time properties, and we give prerequisites for real time programming languages which incorporate our approach. Finally we would ....

[Article contains additional citation context not shown here]

J. Blieberger and R. Lieger. Worst-case space and time complexity of recursive procedures. (to appear), 1994.

....v f 2 implies T (f 1 ) T (f 2 ) ut Thus if we can prove that a certain recursive procedure p is locally time monotonical, then the timing behavior is monotonically distributed too. For complex applications our constraints can be modified by applying parameter space morphisms (for details compare [BL94]) Such a morphism allows for concentrating on those parts of the parameter space that are essential for deriving space and time estimates. As a practical application we present balanced trees which are interesting since operations defined upon them can easily be implemented by recursion and ....

....4 shows all additional functions to be given by the programmer for implementing the recursive procedure insert. By applying the shown morphism, timing properties can be deduced involving the current number of nodes in the tree. More details on real time recursions can be found in [BL95] and in [BL94]. 4 Worst Case Performance Estimates on the Specification Level of Classes In order to study timing analysis of real time objects, we discriminate between the view from inside and the view from outside. The worst case performance (WCP) of the object is estimated by help of a WCP tool which ....

Johann Blieberger and Roland Lieger. Worst-case space and time complexity of recursive procedures. Real-Time Systems, 1994. (to appear).

....p.1 2 J. Blieberger, T. Fahringer, B. Scholz The focus of this paper is on accurate cache behavior analysis. Note that modelling caches is only one performance aspect that must be considered in order to determine execution times. There are many other performance characteristics (Blieberger, 1994; Blieberger and Lieger, 1996; Blieberger, 1997; Fahringer, 1996; Park, 1993; Healy et al. 1995) to be analyzed which however are beyond the scope of this paper. In this paper we introduce a novel approach for deriving a highly accurate analytical function of the precise number of cache hits 2 implied by a program. Our ....

Blieberger, J. and R. Lieger: 1996, `Worst-Case Space and Time Complexity of Recursive Procedures'. Real-Time Systems 11(2), 115--144.

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Blieberger, J., and Lieger, R. Worst-case space and time complexity of recursive procedures. Real-Time Systems 11, 2 (1996), 115--144.

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Blieberger, J., and Lieger, R. Worst-case space and time complexity of recursive procedures. Real-Time Systems 11, 2 (1996), 115--144.

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BL96. Johann Blieberger and Roland Lieger, Worst-case space and time complexity of recursive procedures, Real-Time Systems 11 (1996), no. 2, 115--144.

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