### Table 5 Experimentally derived constants used in the AB cell model equations. Subscript

1996

"... In PAGE 13: ... It is convenient to de ne the model in terms of exponential functions that we denote by: (x1; ; ) def= ?1 e + x1 ?1 The vector eld describing the electrical state of the semipermeable membrane is then given by: _ x1= ?gNa apos;3 2 (x1) x4 (x1 ? vna) ? 2gCax5 (x1 ? vca) (1 + 2x2) ? gKx4 3 (x1 ? vk) ? 2gKCax2 (x1 ? vk) (1 + 2x2) ? gA 3 2 (x1) x6 (x1 ? vk) ? gl (x1 ? vl) _ x2= ?0:003 x2 ? kcax5(x1 ? vca) (1 + 2x2) _ x3= 0:8 h(1 ? x3) apos;3 (x1) ? x3 3 (x1)i _ x4= 0:8 h(1 ? x4) apos;4 (x1) ? x4 4 (x1)i _ x5= ?:042553 hx1 ? + (x1; 5; 5)i _ x6= + (x1; 5; 5) ? x6 where, apos;1 (x1) = ? ( 1 + 1x1) ? (x1; 1; 1) 1 (x1) = 4e 1+ 1x1 apos;2 (x1) = apos;1(x1) ? apos;1(x1) + 1(x1) 2 (x1) = + (x1; 2; 2) apos;3 (x1) = ?0:1 ( 3 + 3x1) ? (x1; 3; 3) 3 (x1) = 0:125e 3+ 3x1 apos;4 (x1) = 0:07e 4+ 4x1 4 (x1) = + (x1; 4; 4) The constants which enter these expressions through the functions were matched with the observed rates of activation and inactivation of ion channels in voltage-clamp experiments from other biological systems. Table5 displays the values used in the numerical tests presented here. In addition, the model contains eleven physiological parameters which describe the various channel conductances and ion-reversal poten- tials.... ..."

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### Table 1 contains enough information to calculate Sraw(AB), as de ned in Equation 5. If aij is the element in the ith row and jth column, then

"... In PAGE 7: ... This is easiest to understand if the partitioning data is presented as a matrix A of intersections between subsets. Table1 shows an hypothetical example with N = 20 and M = 3. Subject A A1 A2 A3 a+j Subject B B1 8 2 1 11 B2 2 3 0 5 B3 2 1 1 4 ai+ 12 6 2 20 Table 1: Intersections between subsets created by subjects A and B.... In PAGE 7: ... Table 1 shows an hypothetical example with N = 20 and M = 3. Subject A A1 A2 A3 a+j Subject B B1 8 2 1 11 B2 2 3 0 5 B3 2 1 1 4 ai+ 12 6 2 20 Table1 : Intersections between subsets created by subjects A and B. The row and column marginal sums from Table 1 can be used to estimate each subject apos;s probability of assigning an image to a given subset.... In PAGE 7: ... Subject A A1 A2 A3 a+j Subject B B1 8 2 1 11 B2 2 3 0 5 B3 2 1 1 4 ai+ 12 6 2 20 Table 1: Intersections between subsets created by subjects A and B. The row and column marginal sums from Table1 can be used to estimate each subject apos;s probability of assigning an image to a given subset. This \Bayesian quot; expected value for element aij is [14]: EB[aij] = ai+a+j N : (13)... In PAGE 12: ... The data used to construct Table 10 were also analyzed using the B statistic. The results appear in Table1 1, and the summary in Table 5. mean median std.... In PAGE 15: ... Table 9 shows the summary of the B agreement between all human and machine partitionings of the images. The full data is found in Table1 4, where extreme values are highlighted by shading. mean median std.... ..."

### Table 6: Equations for the inverse kinematic task. Average Abs. Error Relative Error Method

1995

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### Table 12: Ranking of the ratings (from equation 3) across RED variants and simulation scenarios with AB BP BGBH.

2003

"... In PAGE 15: ... Both pm modes are gen- erally ranked low, but neither distinguishes itself over the other enough to determine a consistent trend across the scenarios. Table12 shows the rankings (based on CABC) for the RED variants when AB BP BGBH (i.e.... ..."

Cited by 4

### Table 12: Ranking of the ratings (from equation 3) across RED variants and simulation scenarios with AB BP BGBH.

"... In PAGE 15: ... Both pm modes are gen- erally ranked low, but neither distinguishes itself over the other enough to determine a consistent trend across the scenarios. Table12 shows the rankings (based on CABC) for the RED variants when AB BP BGBH (i.e.... ..."

### Table 11: Ranking of the ratings (from equation 3) across RED variants and simulation scenarios with AB BP BDBE.

2003

Cited by 4

### Table 11: Ranking of the ratings (from equation 3) across RED variants and simulation scenarios with AB BP BDBE.

### Table 2. Binary material data used in the calculations (a, lattice constant; E0, direct bandgap; 10, spin-orbit splitting; A;B, refractive index parameters in equation (5); k, thermal conductivity).

"... In PAGE 3: ... 3. Material parameters Table2 summarizes all binary material parameters used. Binary lattice constants and energy data are obtained from [7].... ..."

### Table 1: AB algorithm for a URV with a manipulator.

1995

"... In PAGE 26: ...Table1 : (continued.) AB algorithm for a URV with a manipulator.... In PAGE 27: ...Computational Requirements In this section, the computational cost of each equation in Table1 is determined and listed in the last two columns of Table 2 for a URV system with an manipulator containing N revolute joints. In this table, the number of oating point multiplies and divides are considered together under the label of multiplies ( ), and the number of additions and subtractions are combined under the label of additions (+).... ..."

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### Table 1: Axioms of BPA with immediate deadlock 0 abs(x) = 0 abs(x) SAT1

2001

"... In PAGE 13: ... Note that in case of sequential processes, the process that would rst perform actions can always do so, irrespective of the ultimate starting time for the other process. This di erence is apparent from equation SAT40, given in Table 6, which is derivable from the axioms of ACPsat and the standard initialization axioms SI13 and SI16 ( Table1 4, page 22). Axioms SACM3-SACM5 represent the interaction of absolute delay with communication merge.... In PAGE 16: ... From the axioms of BPAsat and the de nitions of time-stamped actions and immediate deadlock, we can easily derive the equations given in Table 9 for closed terms. Axioms A1-A5 from Table1 and the equations from Table 9 together can be considered to form the axioms of BPAsat with time-stamped actions. The di erences with the axioms of BPAs in [6] are all due to the di erent treatment of timing inconsistencies.... In PAGE 18: ... Axiom system of ACPsatI The axiom system of ACPsatI consists of the axioms of ACPsat and the equations given in Table 10. Rw2V R = Rv2V R[v= w] INT1 Rv2; P = INT2 Rv2fpg P = P[p= v] INT3 Rv2V [W P = Rv2V P + Rv2W P INT4 V 6 = ; ) Rv2V R = R INT5 (8p 2 V P[p= v] = Q[p= v]) ) Rv2V P = Rv2V Q INT6 V 6 = ; ) Rv2V v abs( ) = supV abs ( ) INT7 V 6 = ;; sup V 62 V ) Rv2V v abs( ) = supV abs ( ) INT8 sup V 2 V ) Rv2V v abs( ) = supV abs ( ) INT9 Rv2V p abs(P) = p abs(Rv2V P) if p 6 = v INT10 Rv2V (P + Q) = Rv2V P + Rv2V Q INT11 Rv2V (P R) = (Rv2V P) R INT12 Rv2V (P bb R) = (Rv2V P) bb R INT13 Rv2V (P j R) = (Rv2V P) j R INT14 Rv2V (R j P) = R j (Rv2V P) INT15 Rv2V @H(P) = @H(Rv2V P) INT16 p abs(Rv2V P) = Rv2V p abs(P) if p 6 = v SATO6 p abs(Rv2V P) = Rv2V p abs(P) if p 6 = v SAI6 abs(Rv2V P) = Rv2V abs(P) SAU5 Table1 0: Axioms for integration (p 0, v not free in R) Axiom INT1 is similar to the -conversion rule of -calculus. Axioms INT2-INT6 are the crucial axioms of integration.... In PAGE 19: ...tion and the corresponding basic term: Rv2[4:9;5:1) v abs( abs( 0:9 abs( a) k 1:8 abs( b) 2:7 abs( c))) = 5:1 abs( ) Rv2[4:9;5:1) v abs( a) + Rv2[4:9;5:1) v abs( b) = Rv2[4:9;5:1) v abs( a + b) (Rv2[4:9;5:1) v abs( a)) j (Rv2[4:9;5:1) v abs( b)) = Rv2[4:9;5:1) v abs( c) if (a; b) = c (Rv2[4:9;5:1) v abs( a)) j (Rv2[4:9;5:1) v abs( b)) = Rv2[4:9;5:1) v abs( ) if (a; b) unde ned Semantics of ACPsatI The structural operational semantics of ACPsatI is described by the rules for ACPsat and the rules given in Table 11. hP[q= v]; pi a ?! hP0; pi; q 2 V hRv2V P; pi a ?! hP0; pi hP[q= v]; pi a ?! hp; pi; q 2 V hRv2V P; pi a ?! hp; pi hP[q= v]; pi `r ?! hP[q= v]; p + ri; q 2 V hRv2V P; pi `r ?! hRv2V P; p + ri ID(P[q= v]; p) for all q 2 V ID(Rv2V P; p) Table1 1: Rules for integration (a 2 A; r gt; 0; p; q 0) The rules for integration are simple generalizations of the rules for alternative com- position to the in nite case. The panth format does not cover variable binding operators such as integration.... In PAGE 20: ... Axiom system of ACPsatIp The axiom system of ACPsatIp consists of the axioms of ACPsatI and the equations given in Table 12. ps w : G = ps v : G[v= w] SIA1 p abs(ps v : F) = p abs(F[p= v]) SIA2 ps v : (ps w : F) = ps v : F[v= w] SIA3 G = ps v : G SIA4 (8p 2 R 0 p abs(x) = p abs(y)) ) x = y SIA5 p abs( a) x = p abs( a) p abs(x) SIA6 p abs(ps v : F) = p abs(F[0= v]) SIA7 (ps v : F) + G = ps v : (F + v abs(G)) SIA8 (ps v : F) G = ps v : (F G) SIA9 p abs(ps v : F) = ps v : p abs(F) if p 6 = v SIA10 (ps v : F) bb G = ps v : (F bb v abs(G)) SIA11 G bb (ps v : F) = ps v : ( v abs(G) bb F) SIA12 (ps v : F) j G = ps v : (F j v abs(G)) SIA13 G j (ps v : F) = ps v : ( v abs(G) j F) SIA14 @H(ps v : F) = ps v : @H(F) SIA15 abs(ps v : F) = ps v : abs(F) SIA16 Rv2V (ps w : F) = ps w : (Rv2V F) if v 6 = w SIA17 Table1 2: Axioms for standard initial abstraction (p 0, v not free in G) Axioms SIA1 and SIA2 are similar to the - and -conversion rules of -calculus. Axiom SIA3 points out that multiple initial abstractions can simply be replaced by one.... In PAGE 21: ... We use f; g; : : : to denote elements of RTTS (A). In Table1 3, the constants and operators of ACPsatIp are de ned on RTTS (A). We use -notation for functions { here t is a variable ranging over R 0.... In PAGE 22: ... = t : a = t : t abs( a) p abs(f) = t : t abs( p abs(f(0))) f + g = t : (f(t) + g(t)) f g = t : (f(t) g) p abs(f) = t : t abs( p abs(f(t))) p abs(f) = f(p) f k g = t : (f(t) k g(t)) f bb g = t : (f(t) bb g(t)) f j g = t : (f(t) j g(t)) @H(f) = t : @H(f(t)) abs(f) = t : t abs( abs(f(t))) Rv2V (f) = t : Rv2V (f(t)) p s apos; = t : t abs( apos;(t)) Table1 3: De nition of operators on RTTS ( apos; : R 0 ! RTTS (A), a 2 A , p 2 R 0) p abs( p+r abs (x)) = p+r abs ( p abs(x)) SI1 p abs( p+q abs (x)) = p+q abs (x) SI2 p+q abs ( p abs(x)) = p+q abs ( ) SI3 p abs( p+q abs (x)) = p abs( ) SI4 p abs( ) + p abs(x) = p abs(x) SI5 p abs( ) + p abs(x + ) = p abs(x + ) SI6 r abs(x) + = r abs(x) SI7 p abs( q abs(x)) = min(p;q) abs (x) SI8 p abs( q abs( q0 abs(x))) = max(p;q) abs ( q0 abs(x)) SI9 p abs(x bb y) = p abs(x) bb p abs(y) SI10 p abs(x j y) = p abs(x) j p abs(y) SI11 p abs(@H(x)) = @H( p abs(x)) SI12 0 abs( abs(x)) = abs( 0 abs(x)) SI13 r abs( abs(x)) = r abs( ) SI14 abs( r abs(x)) = SI15 r abs( abs(x)) = abs(x) SI16 abs( r abs(x)) = abs(x) SI17 Table 14: Standard initialization axioms (p; q; q0 0; r gt; 0) 3.3 Standard initialization axioms In Table 14, some equations concerning initialization and time-out are given that hold in the model M A, and that are derivable for closed terms of ACPsatIp.... In PAGE 22: ... = t : a = t : t abs( a) p abs(f) = t : t abs( p abs(f(0))) f + g = t : (f(t) + g(t)) f g = t : (f(t) g) p abs(f) = t : t abs( p abs(f(t))) p abs(f) = f(p) f k g = t : (f(t) k g(t)) f bb g = t : (f(t) bb g(t)) f j g = t : (f(t) j g(t)) @H(f) = t : @H(f(t)) abs(f) = t : t abs( abs(f(t))) Rv2V (f) = t : Rv2V (f(t)) p s apos; = t : t abs( apos;(t)) Table 13: De nition of operators on RTTS ( apos; : R 0 ! RTTS (A), a 2 A , p 2 R 0) p abs( p+r abs (x)) = p+r abs ( p abs(x)) SI1 p abs( p+q abs (x)) = p+q abs (x) SI2 p+q abs ( p abs(x)) = p+q abs ( ) SI3 p abs( p+q abs (x)) = p abs( ) SI4 p abs( ) + p abs(x) = p abs(x) SI5 p abs( ) + p abs(x + ) = p abs(x + ) SI6 r abs(x) + = r abs(x) SI7 p abs( q abs(x)) = min(p;q) abs (x) SI8 p abs( q abs( q0 abs(x))) = max(p;q) abs ( q0 abs(x)) SI9 p abs(x bb y) = p abs(x) bb p abs(y) SI10 p abs(x j y) = p abs(x) j p abs(y) SI11 p abs(@H(x)) = @H( p abs(x)) SI12 0 abs( abs(x)) = abs( 0 abs(x)) SI13 r abs( abs(x)) = r abs( ) SI14 abs( r abs(x)) = SI15 r abs( abs(x)) = abs(x) SI16 abs( r abs(x)) = abs(x) SI17 Table1 4: Standard initialization axioms (p; q; q0 0; r gt; 0) 3.3 Standard initialization axioms In Table 14, some equations concerning initialization and time-out are given that hold in the model M A, and that are derivable for closed terms of ACPsatIp.... In PAGE 22: ... = t : a = t : t abs( a) p abs(f) = t : t abs( p abs(f(0))) f + g = t : (f(t) + g(t)) f g = t : (f(t) g) p abs(f) = t : t abs( p abs(f(t))) p abs(f) = f(p) f k g = t : (f(t) k g(t)) f bb g = t : (f(t) bb g(t)) f j g = t : (f(t) j g(t)) @H(f) = t : @H(f(t)) abs(f) = t : t abs( abs(f(t))) Rv2V (f) = t : Rv2V (f(t)) p s apos; = t : t abs( apos;(t)) Table 13: De nition of operators on RTTS ( apos; : R 0 ! RTTS (A), a 2 A , p 2 R 0) p abs( p+r abs (x)) = p+r abs ( p abs(x)) SI1 p abs( p+q abs (x)) = p+q abs (x) SI2 p+q abs ( p abs(x)) = p+q abs ( ) SI3 p abs( p+q abs (x)) = p abs( ) SI4 p abs( ) + p abs(x) = p abs(x) SI5 p abs( ) + p abs(x + ) = p abs(x + ) SI6 r abs(x) + = r abs(x) SI7 p abs( q abs(x)) = min(p;q) abs (x) SI8 p abs( q abs( q0 abs(x))) = max(p;q) abs ( q0 abs(x)) SI9 p abs(x bb y) = p abs(x) bb p abs(y) SI10 p abs(x j y) = p abs(x) j p abs(y) SI11 p abs(@H(x)) = @H( p abs(x)) SI12 0 abs( abs(x)) = abs( 0 abs(x)) SI13 r abs( abs(x)) = r abs( ) SI14 abs( r abs(x)) = SI15 r abs( abs(x)) = abs(x) SI16 abs( r abs(x)) = abs(x) SI17 Table 14: Standard initialization axioms (p; q; q0 0; r gt; 0) 3.3 Standard initialization axioms In Table1 4, some equations concerning initialization and time-out are given that hold in the model M A, and that are derivable for closed terms of ACPsatIp. We will use these axioms in proofs in subsequent sections.... In PAGE 22: ... Notice that the very useful equation p abs( p abs(x)) = p abs(x) is a special case of axiom SI2. We can easily prove by means of the standard initialization axioms, using axioms SIA2 and SIA5 ( Table1 2, page 20), that initial abstraction distributes over +, k, bb and j: (ps v : F) 2 (ps v : F0) = ps v : (F 2 F0) DISTR2... In PAGE 24: ...rel(x) = x SRT1 p rel( q rel(x)) = p+q rel (x) SRT2 p rel(x) + p rel(y) = p rel(x + y) SRT3 p rel(x) y = p rel(x y) SRT4 a + = a A6SRa r rel(x) + = r rel(x) A6SRb x = A7SR p rel( ) = SRTO0 0 rel(x) = SRTO1 r rel( a) = a SRTO2 p+q rel ( p rel(x)) = p rel( q rel(x)) SRTO3 p rel(x + y) = p rel(x) + p rel(y) SRTO4 p rel(x y) = p rel(x) y SRTO5 p rel( ) = p rel( ) SRI0 0 rel(x) = x SRI1 r rel( a) = r rel( ) SRI2 p+q rel ( p rel(x)) = p rel( q rel(x)) SRI3 p rel(x + y) = p rel(x) + p rel(y) SRI4 p rel(x y) = p rel(x) y SRI5 Table1 5: Additional axioms for BPAsrt (a 2 A ; p; q 0; r gt; 0) (a 2 A) and alternative compositions in which the form of the rst operand is p rel(t), can be eliminated in closed terms of BPAsrt. The terms that remain after exhaustive elimination are called the basic terms over BPAsrt.... In PAGE 26: ... ) a a ?! p x a ?! x0 0 rel(x) a ?! x0 x a ?! p 0 rel(x) a ?! p x `r ?! x0 p rel(x) `p+r ??! x0 p gt; 0 p+r rel (x) `r ?! p rel(x) :ID(x) r rel(x) `r ?! x x a ?! x0 x + y a ?! x0; y + x a ?! x0 x a ?! p x + y a ?! p; y + x a ?! p x `r ?! x0; y 6 `r ?! x + y `r ?! x0; y + x `r ?! x0 x `r ?! x0; y `r ?! y0 x + y `r ?! x0 + y0 ID(x); ID(y) ID(x + y) x a ?! x0 x y a ?! x0 y x a ?! p x y a ?! y x `r ?! x0 x y `r ?! x0 y ID(x) ID(x y) x a ?! x0 r rel(x) a ?! x0 x a ?! p r rel(x) a ?! p x `r ?! x0; p gt; 0 p+r rel (x) `r ?! p rel(x0) ID(x) ID( r rel(x)) ID( 0 rel(x)) x a ?! x0 0 rel(x) a ?! x0 x a ?! p 0 rel(x) a ?! p x `r ?! x0; p r p rel(x) `r ?! x0 p gt; 0 p+r rel (x) `r ?! p rel(x) ID(x) ID( 0 rel(x)) Table1 6: Rules for operational semantics of BPAsrt (a 2 A; r gt; 0; p 0) Signature of ACPsrt The signature of ACPsrt is the signature of BPAsrt extended with the parallel composition operator k: Pr Pr ! Pr, the left merge operator bb: Pr Pr ! Pr, the communication merge operator j: Pr Pr ! Pr, the encapsulation operators @H : Pr ! Pr (for each H A), and the relative urgent initialization operator rel : Pr ! Pr. Axioms of ACPsrt The axiom system of ACPsrt consists of the axioms of BPAsrt and the equations given in Table 17.... In PAGE 27: ...if (a; b) = c CF1SR a j b = if (a; b) unde ned CF2SR x k y = (x bb y + y bb x) + x j y CM1 bb x = CMID1 x bb = CMID2 a bb (x + ) = a (x + ) CM2SRID a x bb (y + ) = a (x k (y + )) CM3SRID r rel(x) bb ( rel(y) + ) = SRCM1ID p rel(x) bb ( p rel(y) + p rel(z)) = p rel(x bb z) SRCM2ID (x + y) bb z = x bb z + y bb z CM4 j x = CMID3 x j = CMID4 a x j b = ( a j b) x CM5SR a j b x = ( a j b) x CM6SR a x j b y = ( a j b) (x k y) CM7SR ( rel(x) + ) j r rel(y) = SRCM3ID r rel(x) j ( rel(y) + ) = SRCM4ID p rel(x) j p rel(y) = p rel(x j y) SRCM5 (x + y) j z = x j z + y j z CM8 x j (y + z) = x j y + x j z CM9 @H( ) = D0 @H( a) = a if a 62 H D1SR @H( a) = if a 2 H D2SR @H( p rel(x)) = p rel(@H(x)) SRD @H(x + y) = @H(x) + @H(y) D3 @H(x y) = @H(x) @H(y) D4 rel( ) = SRU0 rel( a) = a SRU1 rel( r rel(x)) = SRU2 rel(x + y) = rel(x) + rel(y) SRU3 rel(x y) = rel(x) y SRU4 Table1 7: Additional axioms for ACPsrt (a; b 2 A ; c 2 A; p 0; r gt; 0) The additional axioms of ACPsrt are just simple reformulations of the additional ax- ioms of ACPsat. That is, constants a (a 2 A ) have been replaced by constants a, and the operators abs, abs and abs have been replaced by rel, rel and rel, respectively.... In PAGE 28: ...rel( a) k 5:1 rel ( b) 0:3 rel ( c) = 5 rel( a 0:1 rel ( b 0:3 rel ( c))) 5:1 rel ( a) k 5 rel( b) 0:3 rel ( c) = 5 rel( b 0:1 rel ( a 0:2 rel ( c))) 5:1 rel ( a) k 4:8 rel ( b) 0:3 rel ( c) = 4:8 rel ( b 0:3 rel ( a c + c a)) Semantics of ACPsrt The structural operational semantics of ACPsrt is described by the rules for BPAsrt and the rules given in Table 18. x a ?! x0; :ID(y) x k y a ?! x0 k y; y k x a ?! y k x0; x bb y a ?! x0 k y x a ?! p; :ID(y) x k y a ?! y; y k x a ?! y; x bb y a ?! y x a ?! x0; y b ?! y0; (a; b) = c x k y c ?! x0 k y0; x j y c ?! x0 k y0 x a ?! p; y b ?! p; (a; b) = c x k y c ?! p; x j y c ?! p x a ?! x0; y b ?! p; (a; b) = c x k y c ?! x0; y k x c ?! x0; x j y c ?! x0; y j x c ?! x0 x `r ?! x0; y `r ?! y0 x k y `r ?! x0 k y0; x bb y `r ?! x0 bb y0; x j y `r ?! x0 j y0 ID(x) ID(x k y); ID(y k x); ID(x bb y); ID(y bb x); ID(x j y); ID(y j x) x a ?! x0; a 62 H @H(x) a ?! @H(x0) x a ?! p; a 62 H @H(x) a ?! p x `r ?! x0 @H(x) `r ?! @H(x0) ID(x) ID(@H(x)) x a ?! x0 rel(x) a ?! x0 x a ?! p rel(x) a ?! p ID(x) ID( rel(x)) Table1 8: Additional rules for ACPsrt (a; b; c 2 A; r gt; 0) Changing from absolute timing to relative timing also leads to a simpli cation of the additional rules for parallel composition, left merge, etc. As in the previous cases, we obtain a model for ACPsrt by identifying bisimilar processes.... In PAGE 29: ... The explicit de nitions needed to show that ACPsrt can be embedded in ACPsatp are given in Table 19. The following lemma presents an interesting property of pro- a = ps v : v abs( a) p rel(x) = ps v : v+p abs (x) p rel(x) = ps v : v+p abs ( v abs(x)) p rel(x) = ps v : v+p abs ( v abs(x)) rel(x) = ps v : v abs( abs(x)) Table1 9: De nitions of relative time operators (a 2 A ) cesses with relative timing. Lemma 4 For each closed term t of ACPsatp generated by the embedded constants and operators of ACPsrt, p abs(t) = p abs(t).... In PAGE 30: ...roof. The proof of this theorem is given in Appendix A.1. The proof is a matter of straightforward calculations. Equations SIAI (page 21) and DISTR2 (page 22), the standard initialization axioms ( Table1 4, page 22), and Lemmas 4 and 5 (page 29-30) are very useful in the proof. 2 5 Discrete time process algebra In this section, we present ACPdat and ACPdrt, discrete time process algebras with absolute timing and relative timing, respectively.... ..."

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