T he composition and physical properties of r I reacting materials influence efficiency and quality when manufacturing chemicals. In large-scale operations, poorly understood secondary reactions perturb primary reactions; composition and other material properties can be only approximately controlled. Attempts to control analytically stoichiometric ratios, material properties, and environmental conditions fail when sensor data are inadequate and an analytical process model is not available. We will consider an application where the heuristic expertise of experienced plant operators is successful. The application of such expertise is inconsistent and incomplete, however, especially in a continuous 24-hour-a-day operation where operator qualifications vary dramatically from shift to shift, and where even the same operator often reacts differently in similar situations.We define process management as a combination of analytical process control and heuristic control that applies human expertise to judge and interpret sensor data, assess ongoing developments, plan appropriate actions, and communicate with operators to give and take advice. Heuristic techniques in process management play a dual role: supervisory control applies heuristic judgment to make decisions about the results provided by analytical or heuristic methods, and direct control interprets sensor data to make control decisions.We will describe a process management system that applies heuristic control to manage the composition of ingoing materials, uses conventional analytical control equipment to maintain a number of physical parameters related to temperature and pressure under which materials react, and supervises both for optimal performance. Real-time operation requires a process management architecture that interleaves process monitoring, 0885-9000/87/0500-0080 $01.0001987 IEEE 80 IEEE EXPERT

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There is a wide variety of areas where matching and unification problems arise:(1.1) DatabasesThe user of a (relational) database [22] may logically AND the" properties she wants to retrieve or else she may be interested in the NATURAL JOIN [17] of two stored relations. In neither case, she would appreciate if she constantly had to take into account that AND is an associative and commutative operation, or that NATURAL JOIN obeys an associative axiom, which may distribute over some other operation [68]. (1.2) Algebra In algebra, a famous decidability problem, which inspite of many attacks remained open for over twenty-five years, has only recently been solved: the monoid problem (also called Lab's Problem in Western Countries, Markov's Problem in Eastern Countries and the Stringunification Problem in Automatic Theorem Proving [33],[34],[35],[69],[60], [48],[73]) is the problem to decide whether or not an equation system over a free semigroup possesses a solution. Last year this problem has beeh shown to be decidable [51]. The monoid problem has important practical applications inter alia for Automatic Theorem Proving (stringunification [69] and second order monadic unification [90],[38]) for Formal Language Theory (the crossreference problem for van Wijngaarden Grammars [88]), and for pattern directed invocation languages in artificial intelligence (see below). (1.3) Information retrieval A patent office may store all recorded electric circuits [11] or all recorded chemical compounds [79] as some graph structure, and the problem of checking whether a given circuit or compound already exists is an instance of a test for graph isomorphism [82],[83],[20]. More generally, if the nodes of such graphs are labelled with universally quantified variables ranging over subgraphs, these problems are practical instances of a graph matching problem.