Approximate Bisimulation and Optimization of Software Programs Based on Symbolic-Numeric Computation

<table class="table-group" id="tab2"><tr><td><table class="table"><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr class="thead"><td align="left">Number of iterations: <svg height="12.3" id="M334" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 14.4375 12.3" width="14.4375" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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q12 68 2 83t-72 22l6 28h257l-7 -28q-62 -7 -76 -21.5t-27 -83.5l-32 -172q29 11 78 46q112 84 217 179q18 16 23.5 25.5t-1 14.5t-26.5 8l-30 4l5 28h249z" id="x1D43E"></path></g>
</svg></td><td align="center">Initial states</td><td align="center">Solutions</td><td align="center">Minimum</td></tr><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr><td align="left"><span style="width: 42.012501px;"><svg height="12.3" id="M335" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 42.012501 12.3" width="42.012501" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.625,11.675)"><path d="M764 650l-7 -26q-61 -10 -91.5 -22.5t-76.5 -48.5l-235 -184q104 -152 208 -276q31 -37 54.5 -48.5t68.5 -16.5l-7 -28h-156q-138 170 -213 284q-19 29 -33.5 35t-33.5 -7l-29 -173q-15 -75 -5.5 -90.5t74.5 -20.5l-5 -28h-260l7 28q58 5 74 21.5t30 89.5l70 378
q12 68 2 83t-72 22l6 28h257l-7 -28q-62 -7 -76 -21.5t-27 -83.5l-32 -172q29 11 78 46q112 84 217 179q18 16 23.5 25.5t-1 14.5t-26.5 8l-30 4l5 28h249z" id="x1D43E"></path></g><g transform="matrix(.017,-0,0,-.017,18.525,11.675)"><path d="M535 323h-483v50h483v-50zM535 138h-483v50h483v-50z" id="x3D"></path></g><g transform="matrix(.017,-0,0,-.017,33.229,11.675)"><path d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" id="x31"></path></g>
</svg></span></td><td align="center">(1, 1, 1, 1)</td><td align="center">(0.05, 0.84, 1, 0.84)</td><td align="center"><span style="width: 88.625px;"><svg height="12.2375" id="M336" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 88.625 12.2375" width="88.625" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.625,11.413)"><path d="M535 230h-483v50h483v-50z" id="x2212"></path></g><g transform="matrix(.017,-0,0,-.017,10.603,11.413)"><path d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" id="x31"></path></g><g transform="matrix(.017,-0,0,-.017,18.763,11.413)"><path d="M113 -12q-24 0 -39.5 16t-15.5 42q0 24 16 40.5t40 16.5t40 -16.5t16 -40.5q0 -26 -16 -42t-41 -16z" id="x2E"></path></g><g transform="matrix(.017,-0,0,-.017,22.638,11.413)"><path d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105
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</svg></span></td></tr><tr class="table-tr"><td colspan="4"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Mathematical Problems in Engineering

tab2

Table 2

Table 2: Approximate Bisimulation and Optimization of Software Programs Based on Symbolic-Numeric Computation 