A Novel Algorithm for Intrusion Detection Based on RASL Model Checking

Algorithm 2

Constructing discrete timed automata for RASL formula.

function CONSTRUCT (𝐺)

 /* pre-condition: 𝐺 = (CL(P), EL(P), X) is an TNFG of RASL formula P*/

 /* post-condition: CONSTRUCT constructs a timed automaton from TNFG of formula P*/

begin function

 𝑆∶={𝑃};𝑆₀∶={𝑃};Σ∶=𝜙;𝐸∶=𝜙;

 CL∶=CL(𝑃) /* CL denotes acceptance state set */

 For all 𝑄∈CL(𝑃) do If 𝑄 is labeled F then CL∶=CL/{𝑄} /*Acceptance state set doesn’t contain the circulate

 nodes passed by finite times */

 CL∶=CL/{𝜀} /*Acceptance state set doesn’t contain the final states */

 while  ∃𝑒𝑙=(𝑄,𝑄_𝑐𝑖,𝑄_𝑛𝑖,𝛿,𝜆)∈EL(𝑃)/*for every non-terminal edge of TNFG*/

 do  𝑠∶=𝑄;𝑠^′∶=𝑄_𝑛𝑖;𝑎∶=𝑄_𝑐𝑖;𝑒∶=(𝑠,𝑠^′,𝑎,𝛿,𝜆);𝐸∶=𝐸∪{𝑒}; /*add transition rules to timed automaton*/

  𝑆∶=𝑆∪{𝑠,𝑠^′};Σ∶=Σ∪{𝑎}; /*add state and input alphabet to timed automaton

 end while

 while  ∃𝑒𝑙=(𝑄,𝑄_𝑒,𝜀,𝛿,𝜆)∈EL(𝑃) /*for every terminal edge of TNFG*/

 do  𝑠∶=𝑄;𝑠^′∶=𝜀;𝑎∶=𝑄_𝑒;𝑒∶=(𝑠,𝑠^′,𝑎,𝛿,𝜆);𝐸∶=𝐸∪{𝑒}; /*add transition rule to timed automaton*/

  𝑆∶=𝑆∪{𝑠,𝑠^′};Σ∶=Σ∪{𝑎}; /*add state and input alphabet to timed automaton*/

 end while

 𝐹∶={𝜀};𝐴𝐶∶=CL;/*set of final states and set of acceptance states*/

 return  𝐴=(Σ,𝑆,𝑆₀,𝐸,𝑋,𝐹,𝐴𝐶);

end function

Construction Procedure (P)

 (1) Build the TNFG of P, 𝐺 = (CL(P); EL(P), X), by algorithm TNFG(P);

 (2) Obtain the timed automaton, 𝐴=(Σ,𝑆,𝑆₀,𝐸,𝑋,𝐹,𝐴𝐶), by algorithm CONSTRUCT(𝐺^′).