"... In PAGE 11: ... We use the dictionary words that collects 45000 words. Table1 summarises the results (time limit is set to 1 hour). The initial propagation of the automaton is costly (initialisation of the Qij lists).... ..."

"... In PAGE 10: ... In many cases the overhead for checking 00 in addition to 0 is well within the noise margin. Table2 compares the use of reachability analysis of the automaton when search- ing for the values of m and n (columns labeled Yes) to its omission (columns labeled No). Reachability analysis of the automaton usually reduces runtime, but it does not help in reducing the values of m and n.... ..."

"... In PAGE 5: ... 3.1 Single Cell Hybrid Automaton Proposition 1 #28Existence of equilibria#29 The existence of equilibria #28v #03 D ;v #03 N #29 of H 1 , given in Table1 , depend on the switching threshold h D , and the existence conditions are as given in Table 2. Proof: The proof is constructed by formulating an algebraic test for the existence of equilibria in each mode #28i.... ..."

"... In PAGE 25: ... Actual dynamical implementation of the correction mechanism is a focus of current research. The Input Map for the Dynamical Automaton we used to model transitive sentences with relative clause modi ers is shown in Table3 . The automaton uses 9 partition states and moves around on a 3-dimensional fractal.... In PAGE 30: ...De nition Start (1/2, 1/2, 1/2) Comp1 (0, 0, 0) + opencube Comp2 (0, 1/2, 0) + opencube V1 (1/2, 0, 0) + opencube V2 (1/2, 1/2, 0) + opencube NObj1 (0, 0, 1/2) + opencube NObj2 (0, 1/2, 1/2) + opencube NSubj1 (1/2, 0, 1/2) + opencube NSubj2 (1/2, 1/2, 1/2) + opencube Note: opencube is the set f(x; y; z) : 0 lt; x lt; 1=2; 0 lt; y lt; 1=2; 0 lt; z lt; 1=2g. Note: Compartment A as labelled in Table3 is the union of the compartments A1 and A2 shown above for A 2 fComp; V; NObj; NSubjg. Table 4: Dynamical Automaton 2: compartment de nitions.... ..."

"... In PAGE 23: ... The transition will be made on a constant true condition and the current token will be available to be used on the next transition as needed. Example 11: Figure 12 and Table2 displays the T T and CT tables that controls the NFA in Figure 11. Keywords in the regular expression of conditions are mapped by LSF P arser into tran- sitions in TT labeled by prede ned programs.... In PAGE 26: ...final) return true 19 else ulex = marker; return false Observation: to decrease nondeterminism we remove the useless attempts by looking at the class speci er of the ulex before moving to the next state thus making sure that the current state has a viable transition. Example 12: Consider the input text : : : sam gt; 34 : : : and the conditional automaton speci ed in Example 8, whose condition table is Table2 , whose transition table is in Fig- ure 12, and whose graphical representation can be seen in Figure 11. Assume that this text has been consumed by the FLS and the portion sam gt; 34 is still available in UniBuf as shown in Figure 13.... ..."

"... In PAGE 17: ...Original SAT Model New SAT Model (v;b; r; k; )) Walksat/SKC ips Walksat/SKC Walksat/MVW 7,7,3,3,1 51412 406 117 6,10,5,3,2 121259 637 248 9,12,4,3,1 6382697 3102 366 11,11,5,5,2 | 8383 6547 7,14,6,3,2 2028247 1754 339 13,13,4,4,1 | 3725 1216 8,14,7,4,3 | 7644 2385 10,15,6,4,2 | 33913 2959 9,18,8,4,3 | 36046 9386 6,20,10,3,4 | | 362 7,21,9,3,3 | | 453 9,24,8,3,2 | | 664 7,28,12,3,4 | | 509 6,30,15,3,6 | | 602 7,35,15,3,5 | | 606 6,40,20,3,8 | | 752 Table1 . Comparison of results from [10] with the new model Acknowledgement This work was supported by the Boole Centre for Research in Informatics, Uni- versity College, Cork, Ireland, and is based in part upon works supported by the Science Foundation Ireland under Grant No.... In PAGE 39: ...dom=wdeg Instances min-conflts max-confts ratio min-confts max-confts ratio h40-8-753-0:1i cpu 42:0 51:4 1:22 34:5 41:6 1:20 ccks 22M 27M 1:22 20M 24M 1:20 nodes 43;269 55;558 1:28 38;104 48;158 1:59 h40-11-414-0:2i cpu 30:9 35:0 1:13 29:4 32:7 1:11 ccks 26M 29M 1:11 26M 29M 1:11 nodes 58;955 70;007 1:18 58;055 67;905 1:17 h40-16-250-0:35i cpu 22:1 28:9 1:30 21:0 26:6 1:26 ccks 30M 40M 1:33 30M 37M 1:23 nodes 59;669 83;445 1:39 56;036 75;025 1:33 h40-25-180-0:5i cpu 33:1 37:1 1:12 28:6 30:0 1:04 ccks 62M 67M 1:08 55M 57M 1:03 nodes 85;122 98;519 1:15 69;805 78;005 1:11 h40-40-135-0:65i cpu 25:9 34:6 1:33 20:0 25:1 1:25 ccks 68M 89M 1:30 53M 66M 1:24 nodes 52;622 74;592 1:41 36;571 49;211 1:34 h40-80-103-0:8i cpu 25:8 52:8 2:04 15:3 36:3 2:37 ccks 98M 193M 1:96 59M 133M 2:25 nodes 29;989 72;841 2:42 16;163 45;177 2:79 h40-180-84-0:9i cpu 113:1 121:3 1:07 40:6 44:6 1:09 ccks 554M 587M 1:05 217M 231M 1:06 nodes 76;788 85;482 1:11 20;077 22;557 1:12 Table1 . MAC with d-way branching, dom=ddeg and dom=wdeg dom=ddeg dom=wdeg Instances min-confts max-confts ratio minconfts max-confts ratio h40-8-753-0:1i cpu 29:3 35:8 1:22 28:9 28:4 0:98 ccks 22M 27M 1:22 24M 23M 0:95 nodes 43;268 55;557 1:28 45;650 46;645 1:02 h40-11-414-0:2i cpu 23:0 25:9 1:12 26:1 27:3 1:04 ccks 26M 29M 1:11 32M 33M 1:03 nodes 59;002 70;026 1:18 69;111 76;941 1:11 h40-16-250-0:35i cpu 18:5 24:5 1:32 23:0 24:4 1:06 ccks 30M 40M 1:33 39M 41M 1:05 nodes 59;773 83;531 1:18 72;555 82;459 1:13 h40-25-180-0:5i cpu 28:8 31:9 1:33 28:5 30:7 1:07 ccks 62M 67M 1:08 65M 68M 1:04 nodes 85;187 98;548 1:15 80;017 91;464 1:14 h40-40-135-0:65i cpu 21:4 28:6 1:33 19:8 19:6 0:98 ccks 68M 89M 1:30 65M 64M 0:98 nodes 52;569 74;544 1:41 44;120 46;573 1:05 h40-80-103-0:8i cpu 20:4 42:3 2:07 12:6 18:6 1:47 ccks 98M 193M 1:96 64M 89M 1:39 nodes 29;931 72;747 1:41 16;168 28;087 1:73 h40-180-84-0:9i cpu 85:0 92:0 1:08 26:4 27:1 1:02 ccks 553M 587M 1:06 192M 193M 1:00 nodes 76;489 85;255 1:11 15;835 16;566 1:04 Table 2.... In PAGE 91: ... This approach often leads to a non-chronological backtracking operation, jumping back more than just one level and making con ict-driven learning combined with non-chronological backtracking a powerful mechanism to prune large parts of the search space [24]. 4 Integrating interval constraint propagation and SAT By combining interval constraint propagation with an interval splitting scheme to obtain a branch-and-prune algorithm, as shown on the left of Table1 , a con- straint solving algorithm for constraints over the reals incorporating transcen- dental functions can be achieved being based on interval splitting over real-valued intervals as a branching step and on ICP as a forward inference step, it does closely resemble the core algorithm of DPLL SAT solving. In fact, DPLL-SAT can be viewed as its counterpart over the Boolean intervals IB, where again inter- val splitting is the decision step and Boolean constraint propagation in the form of unit propagation provides the forward inference mechanism, cf.... In PAGE 91: ... In fact, DPLL-SAT can be viewed as its counterpart over the Boolean intervals IB, where again inter- val splitting is the decision step and Boolean constraint propagation in the form of unit propagation provides the forward inference mechanism, cf. right-hand side of Table1 . This similarity motivates a tighter integration of propositional SAT and arithmetic reasoning than in classical lazy theorem proving, cf.... In PAGE 92: ... Split b into subintervals b1 and b2, set L := L n fbg [ fb1; b2g, goto 2. Table1 .... In PAGE 112: ...Table1 provides an overview of the results in terms of the number of instances unsolved within the time limit (#time- outs) and the average cpu time in seconds (avg time) computed from instances solved by all three methods. Figures 3 and 4 represent scatter plots displaying pairwise com- parisons for dom=ddeg and dom=wdeg.... In PAGE 112: ... When we further exploit nogood recording, the gain is about 10%. MAC + RST + RST + NG dom=ddeg #timeouts 365 378 337 avg time 125:0 159:0 109:1 brelaz #timeouts 277 298 261 avg time 85:1 121:7 78:2 dom=wdeg #timeouts 140 123 121 avg time 47:8 56:0 43:6 Table1 . Number of unsolved instances and average cpu time on the 2005 CSP competition benchmarks, given 30 minutes CPU.... In PAGE 127: ... We use the dictionary words that collects 45000 words. Table1 summarises the results (time limit is set to 1 hour). The initial propagation of the automaton is costly (initialisation of the Qij lists).... ..."

"... In PAGE 9: ... Semantics of monitored executions 3.3 Example of monitored execution Table1 is an example of monitored execution. The monitored program is given in column Program P .... ..."