### TABLE 1. Levels of Abstraction and their interpretation.

### Table 1: Results of abstract interpretation for the quicksort program

1992

Cited by 110

### Table 1. Result of abstract interpretation for example flowchart.

2003

"... In PAGE 2: ... The system is solved by fixed-point iteration for the simplified system, which converges in nine iterations. The result is shown in Table1 . (BQ stands for the universal set: CB BC BP BQ thus means that we allow any starting state in the analysis.... ..."

Cited by 22

### Table 1. Result of abstract interpretation for example flowchart.

2003

"... In PAGE 14: ... Note also that since many of the asserted functions are common to various tasks, inaccuracies in assumptions are propagated among tasks. As an example, let us present results concerning task Mil_Bus_Manager ( Table1 ). This task manages the bus that connects the different satellite payloads, and is the largest and most complex task of the CDMU application.... In PAGE 14: ... This task manages the bus that connects the different satellite payloads, and is the largest and most complex task of the CDMU application. Table1 . WCET calculation results Task WCET given by Bound-T (ms) WCET reported in design documents (ms) Mil_Bus_Manager 15.... In PAGE 14: ... WCET calculation results Task WCET given by Bound-T (ms) WCET reported in design documents (ms) Mil_Bus_Manager 15.79 20 Table1 reports two different values: the WCET estimated by Bound-T, and the WCET reported in the design documents of the CDMU application. The latter value is mainly based on in-service history information of previous missions of similar applications.... In PAGE 14: ... The latter value is mainly based on in-service history information of previous missions of similar applications. As shown in Table1 , the WCET given by Bound-T (about 16 ms) was slightly under the value reported in the design documents (20 ms). 5.... In PAGE 59: ...#Variables #Constraints CFG/TGs 67 114 ECFG 43 32 Table1 : ILP formulations of matsum (branch pre- diction modeling) with the two approaches as always miss, then the self loop edge e1 of A, which results in cache hit, is trimed off from the CCG. This results in the flow increase of e2 and consequently more cache misses for B.... In PAGE 59: ...06s Table 2: Impact of ILP problem size and nature on solving time (results of the CFG/TGs approach) graphs) and the other one using single ECFG. In Table1 , the numbers of variables and constraints of the matsum benchmark (modeling branch predic- tion) are presented. Obviously, the ECFG has less variables and constraints than the CFG/TGs.... In PAGE 67: ... We propose to collect an agreed set of requirements from the WCET Community on the information needed to perform WCET analysis with the aim of producing a white paper to influence compiler manufacturers and vendors to make such information available. Table1 , below, lists the items we have collected so far. ordered by requirement category.... In PAGE 67: ... Other future work includes finding collateral benefits, prioritizing the requirements, and defining the data formats and other interfaces for implementing the requirements. Table1 . Compiler and linker support for timing analysis Requirement category Property, mapping or control Examples Supported analyses Properties on source-code level Tree structure of the code Intra-procedural control structures: sequence, conditional, switch/case, loop, exception.... In PAGE 89: ...ending code). # insts crc CRC computation 54 790 fft1 FFT using Cooly-Turkey algorithm 3163 jfdctint JPEG slow-but-accurate integer implementation of the forward DCT 5828 lms LMS adaptive signal enhancement 535 985 ludcmp LU decomposition 7 797 Table1 . Benchmark applications (from the SNU suite) 4.... In PAGE 100: ... The system is solved by fixed-point iteration for the simplified system, which converges in nine iterations. The result is shown in Table1 . (BQ stands for the universal set: CB BC BP BQ thus means that we allow any starting state in the analysis.... ..."

### Table 1. Example abstract state sets and their concretizations Abstract state elements are represented by their interpretations of D4 and D5. The terms are interpreted over CI.

2004

"... In PAGE 5: ... As an example, our two predicates AUD4 and AUD5 generate an abstract space consisting of four elements, which we denote FF, FT, TF, and TT, according to the interpretations assigned to D4 and D5. There are then 16 possible abstract state sets, some of which are shown in Table1 . In this table, abstract state sets are represented both by Boolean formulas over D4 and D5, and by enumerations... In PAGE 6: ... Consider our example system with predicates AUD4 and AUD5. Table1 shows some example abstract state sets CBBT and their concretizations ADB4CBBTB5. As the first three examples show, some (altogether 6) nonempty abstract state sets have empty concretizations, because they constrain DC to be either always negative or always non-negative.... In PAGE 8: ...unctions CU satisfying CUB4D9B5 AL BC B8 D9 AL BC. Let CW denote the value of BY in the next state. If input CX is A0BD, we would CWB4A0BDB5 BP CUB4BCB5 AL BC, but we can still guarantee that CWB4D9B5 AL BC for D9 AL BC. Applying the abstraction function, we get CABD BT characterized by the formula D4 CN BMD5 (see Table1 .) For the second iteration, the abstract state set characterized by the formula D4 CN BMD5 concretizes to the set of functions CU satisfying CUB4D9B5 AL BC when D9 AL BC, and this condition must hold in the next state as well.... In PAGE 8: ... The property holds for the concrete system when BKCGAWA3B4D7B5 holds for every reachable concrete state D7 BE CABV. Table1 shows the concrete system properties given by different abstract state formulas AW. Theorem 2.... ..."

Cited by 19

### Table 1. Example abstract state sets and their concretizations Abstract state elements are represented by their interpretations of D4 and D5. The terms are interpreted over CI.

2004

"... In PAGE 5: ... As an example, our two predicates AUD4 and AUD5 generate an abstract space consisting of four elements, which we denote FF, FT, TF, and TT, according to the interpretations assigned to D4 and D5. There are then 16 possible abstract state sets, some of which are shown in Table1 . In this table, abstract state sets are represented both by Boolean formulas over D4 and D5, and by enumerations... In PAGE 6: ... Consider our example system with predicates AUD4 and AUD5. Table1 shows some example abstract state sets CBBT and their concretizations ADB4CBBTB5. As the first three examples show, some (altogether 6) nonempty abstract state sets have empty concretizations, because they constrain DC to be either always negative or always non-negative.... In PAGE 8: ...unctions CU satisfying CUB4D9B5 AL BC B8 D9 AL BC. Let CW denote the value of BY in the next state. If input CX is A0BD, we would CWB4A0BDB5 BP CUB4BCB5 AL BC, but we can still guarantee that CWB4D9B5 AL BC for D9 AL BC. Applying the abstraction function, we get CABD BT characterized by the formula D4 CN BMD5 (see Table1 .) For the second iteration, the abstract state set characterized by the formula D4 CN BMD5 concretizes to the set of functions CU satisfying CUB4D9B5 AL BC when D9 AL BC, and this condition must hold in the next state as well.... In PAGE 8: ... The property holds for the concrete system when BKCGAWA3B4D7B5 holds for every reachable concrete state D7 BE CABV. Table1 shows the concrete system properties given by different abstract state formulas AW. Theorem 2.... ..."

Cited by 19

### Table 1. Example abstract state sets and their concretizations Abstract state elements are represented by their interpretations of D4 and D5. The terms are interpreted over CI.

2004

"... In PAGE 5: ... As an example, our two predicates AUD4 and AUD5 generate an abstract space consisting of four elements, which we denote FF, FT, TF, and TT, according to the interpretations assigned to D4 and D5. There are then 16 possible abstract state sets, some of which are shown in Table1 . In this table, abstract state sets are represented both by Boolean formulas over D4 and D5, and by enumerations... In PAGE 6: ... Consider our example system with predicates AUD4 and AUD5. Table1 shows some example abstract state sets CBBT and their concretizations ADB4CBBTB5. As the first three examples show, some (altogether 6) nonempty abstract state sets have empty concretizations, because they constrain DC to be either always negative or always non-negative.... In PAGE 8: ...unctions CU satisfying CUB4D9B5 AL BC B8 D9 AL BC. Let CW denote the value of BY in the next state. If input CX is A0BD, we would CWB4A0BDB5 BP CUB4BCB5 AL BC, but we can still guarantee that CWB4D9B5 AL BC for D9 AL BC. Applying the abstraction function, we get CABD BT characterized by the formula D4 CN BMD5 (see Table1 .) For the second iteration, the abstract state set characterized by the formula D4 CN BMD5 concretizes to the set of functions CU satisfying CUB4D9B5 AL BC when D9 AL BC, and this condition must hold in the next state as well.... In PAGE 8: ... The property holds for the concrete system when BKCGAWA3B4D7B5 holds for every reachable concrete state D7 BE CABV. Table1 shows the concrete system properties given by different abstract state formulas AW. Theorem 2.... ..."

Cited by 19

### Table 3.2: The Abstract Functions and their Types for the Generic Interpreter Model.

1993

### Table 1.1: Comparison of abstract interpretation to other methods

2003

### Table 2: The modules where the abstract task-execution functions are interpreted.

1994