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sav07_lecture_20 [2007/06/05 11:02] kremena.diatchka |
sav07_lecture_20 [2007/06/05 19:04] kremena.diatchka |
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| - must follow protocol: (open (read+write)* close)* | - must follow protocol: (open (read+write)* close)* | ||
| - must follow protocol: (startLog stopLog)* | - must follow protocol: (startLog stopLog)* | ||
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| Let $S$ be the set of program states and $V$ be the set of vertices in the control flow graph. Then we can describe a point in the program as: | Let $S$ be the set of program states and $V$ be the set of vertices in the control flow graph. Then we can describe a point in the program as: | ||
| - | $(s,c)$ | + | $(c,s)$ |
| - | where $s \in S, c \in V$ | + | where $c \in V$, $s \in S, |
| Consider the following example: | Consider the following example: | ||
| - | Picture will go here. | + | {{lect20_big_step.png|}} |
| $p()$ is a procedure which can described by the relation $r$: $\{(x,y), (x',y') | x'=100 \wedge y'=y\}$ | $p()$ is a procedure which can described by the relation $r$: $\{(x,y), (x',y') | x'=100 \wedge y'=y\}$ | ||
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| In order to define procedure contracts for ''readContent()'' and ''p1()'' to ensure that this property is satisfied, we introduce an object called ''FileState'' which has a typestate. In typestate systems, the type of an object is allowed to change during its lifetime in the computation. In the paper [[http://lara.epfl.ch/~kuncak/papers/LamETAL05GeneralizedTypestateCheckingDataStructureConsistency.pdf|Generalized typestate checking for data structure consistency]], it says that "unlike standard type systems, typestate systems can enforce safety properties that depend on changing object states". | In order to define procedure contracts for ''readContent()'' and ''p1()'' to ensure that this property is satisfied, we introduce an object called ''FileState'' which has a typestate. In typestate systems, the type of an object is allowed to change during its lifetime in the computation. In the paper [[http://lara.epfl.ch/~kuncak/papers/LamETAL05GeneralizedTypestateCheckingDataStructureConsistency.pdf|Generalized typestate checking for data structure consistency]], it says that "unlike standard type systems, typestate systems can enforce safety properties that depend on changing object states". | ||
| - | Therefore ''FileState'' has type ''file'' and two states, ''open'' and ''closed''. Using this notion, we can write the procedure contracts for the two methods as follows: | + | Therefore ''FileState'' has type ''file'' and two states, ''open'' and ''closed''. |
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| + | {{lect20_fsm2.png|}} | ||
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| + | Using this notion, we can write the procedure contracts for the two methods as follows: | ||
| readContent() | readContent() | ||
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| modifies: FileState | modifies: FileState | ||
| ensures: FileState = open | ensures: FileState = open | ||
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| === Convergence of automata for reachable configurations === | === Convergence of automata for reachable configurations === | ||
| - | One of the main results of this paper is an algorithm which, given a set of states S, computes the set of all predecessors of S, denoted by $pre^{*}(S)$. The states in $pre^{*}(S)$ are regular, i.e. they can be represented using a finite state automaton. | + | One of the main results of this paper is an algorithm which, given a set of states $S$, computes the set of all predecessors of $S$, denoted by $pre^{*}(S)$. The states in $pre^{*}(S)$ are regular, i.e. they can be represented using a finite state automaton. |
| In the paper, a pushdown system is defined as a triplet $\mathcal{P} = (P, \Gamma, \Delta)$ where | In the paper, a pushdown system is defined as a triplet $\mathcal{P} = (P, \Gamma, \Delta)$ where | ||
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| $\mathcal{A}$ accepts or recognizes a configuration $\langle p^{i},w \rangle$ if $s^{i} \stackrel{w}{\longrightarrow} q$ for some $q \in F$. The set of configurations recognized by $\mathcal{A}$ is denoted $Conf(\mathcal{A})$. As stated before, a set of configurations is regular if it recognized by some MA. | $\mathcal{A}$ accepts or recognizes a configuration $\langle p^{i},w \rangle$ if $s^{i} \stackrel{w}{\longrightarrow} q$ for some $q \in F$. The set of configurations recognized by $\mathcal{A}$ is denoted $Conf(\mathcal{A})$. As stated before, a set of configurations is regular if it recognized by some MA. | ||
| + | Section 2.2 of the paper explains how, given a regular set of configurations $C$ of a PDS $\mathcal{P}$ recognized by an MA $\mathcal{A}$, we can construct another MA $\mathcal{A}_{pre*}$ recognizing $pre^{*}(C)$ (refer to paper for details). | ||
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| + | So the idea in the end is to make $C$ include those undesirable (error) states, and then check whether $pre^{*}(C)$ includes the starting state configurations (in other words, whether any of the error states are reachable from the start state). | ||
| ==== References ==== | ==== References ==== | ||