解简单文字方程的难度
The Hardness of Solving Simple Word Equations
摘要：
研究了正则序词方程类。在这样的方程中，每个变量在每一侧最多出现一次，并且变量在两侧出现的顺序是保留的（变量可以，然而，由潜在的不同常数因子分开）。令人惊讶的是，我们得到，解决这样简单的方程，即使双方包含完全相同的变量，是NP-难的。通过对更一般的二次方程的极小解的组合结构的考虑，我们得到了正则序方程的可满足性问题是NP问题。最后，我们还表明，一个相关的类简单的字方程，推广一元方程，是在P。
英文摘要：
We investigate the class of regular-ordered word equations. In such equations, each variable occurs at most once in each side and the order of the variables occurring in both sides is the preserved (the variables can be, however, separated by potentially distinct constant factors). Surprisingly, we obtain that solving such simple equations, even when the sides contain exactly the same variables, is NP-hard. By considerations regarding the combinatorial structure of the minimal solutions of the more general quadratic equations we obtain that the satisfiability problem for regular-ordered equations is in NP. Finally, we also show that a related class of simple word equations, that generalises one-variable equations, is in P.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
