Computational Intelligence, Volume 21, Number 4, 2005
A CONSTRAINED ARCHITECTURE FOR LEARNING
AND PROBLEM SOLVING
RANDOLPH M. JONES
Soar Technology, Inc., Waterville, ME 04901
PAT LANGLEY
Computational Learning Laboratory, Center for the Study of Language and Information,
Cordura Hall, Stanford University, Stanford, CA 94305
This paper describes EUREKA, a problem-solving architecture that operates under strong constraints on its
memory and processes. Most significantly, EUREKA does not assume free access to its entire long-term memory.
That is, failures in problem solving may arise not only from missing knowledge, but from the (possibly temporary)
inability to retrieve appropriate existing knowledge from memory. Additionally, the architecture does not include
systematic backtracking to recover from fruitless search paths. These constraints significantly impact EUREKA’s
design. Humans are also subject to such constraints, but are able to overcome them to solve problems effectively. In
EUREKA’s design, we have attempted to minimize the number of additional architectural commitments, while staying
faithful to the memory constraints. Even under such minimal commitments, EUREKA provides a qualitative account
of the primary types of learning reported in the literature on human problem solving. Further commitments to the
architecture would refine the details in the model, but the approach we have taken de-emphasizes highly detailed
modeling to get at general root causes of the observed regularities. Making minimal additional commitments to
EUREKA’s design strengthens the case that many regularities in human learning and problem solving are entailments
of the need to handle imperfect memory.
Key words: human and machine learning, problem solving, cognitive architecture, memory limitations,
qualitative cognitive model.
1. INTRODUCTION
The subject of problem solving has been studied from a computational standpoint since
the earliest days of research in artificial intelligence. Both human and computational problem
solvers have limited resources, perhaps the most important of which is time. Problem solutions
are only useful if they can be discovered in a timely manner. Thus, intelligent problem-solving
systems have typically been designed with efficiency in mind, in that they use intelligent
methods to control otherwise intractable searches through a problem space. In addition,
learning in this framework usually involves improving the efficiency of the problem-solving
methods.
Although efficiency concerns are important for both computational and psychological
models, other types of limitations on problem solvers have not received as much attention.
The research we report in this paper focuses on the impact of memory limitations on problem
solving and learning. We have created a problem-solving architecture that imposes signifi-
cant constraints on memory. Most significantly, the model does not have free access to its
memory. That is, the problem solver may fail to solve some problems because it does not re-
trieve the appropriate knowledge, even if that knowledge exists in memory. Additionally, the
architecture cannot rely on standard backtracking to search a problem space in a systematic
manner; rather, it must begin every new search path by restarting from the top-level goal of
the current problem.
We have selected these constraints because we believe they have a major impact on
how humans learn and solve problems. We have tested this hypothesis by building minimal
additional constraints in the architecture. The result is an architecture that does not provide
detailed, quantitative accounts of specific human behaviors, but does provide qualitative
explanations for general regularities in human learning. By modeling these regularities in a
simple way, this minimalist architecture provides evidence that the regularities derive from the
C© 2005 Blackwell Publishing, 350 Main Street, Malden, MA 02148, USA, and 9600 Garsington Road, Oxford OX4 2DQ, UK.

CONSTRAINED ARCHITECTURE 481
need to deal with memory constraints, rather than arising from more complicated architectural
representations and processes.
To develop an architecture centered on the assumed memory constraints required devel-
oping an appropriate framework for problem solving, integrating it with a model of memory,
and implementing a learning algorithm based on the memory model. We have accomplished
this effort by developing a system called EUREKA. Our evaluation of this model focuses on
qualitatively replicating robust psychological findings on learning in problem solving.
The following section describes the overall framework of EUREKA’s performance mech-
anism, its memory module, and its learning algorithm, together with some details of the
model’s actual implementation. We then present some experimental results on the system’s
behavior, and relate these results to well-known learning phenomena in the area of human
problem solving. In the final section, we discuss these results and the system’s relationship
to other research.
2. AN OVERVIEW OF EUREKA
In this section, we provide a general overview of the EUREKA architecture and its im-
plementation in a computer program. The memory limitations we have mentioned suggest
another important design aspect of EUREKA: the system treats all problem solving as a form
of analogical reasoning. Thus, it does not contain distinct methods for standard problem solv-
ing and analogical problem solving, like many other systems (e.g., Anderson 1983; Holland
et al. 1986). However, unlike most case-based reasoners (e.g., Hammond 1988; Kolodner,
Simpson, and Sycara 1985) and other strictly analogical problem solvers (Carbonell 1986),
EUREKA takes advantage of the benefits provided by a standard problem-space search. We
first discuss how these assumptions influenced our overall design decisions, and then present
EUREKA’s implementation in more detail.
2.1. Top-Level Design Decisions
To address the issue of memory limitations in problem solving, we focused on three
distinct pieces of the system. These pieces include the problem-solving engine, the memory
module, and the methods for learning from experience.
To take the role of memory seriously, we designed EUREKA to reason completely by
analogy, but to solve problems by searching through a problem space. This contrasts with
most existing analogical problem solvers, such as case-based reasoners, which attempt to
solve new problems by transforming solutions from old problems. Such systems retrieve an
entire problem solution from memory and use it as the basis for solving the current problem.
In contrast, EUREKA creates analogies to individual subproblems each time it confronts
a problem-solving decision (which typically occurs many times during a single problem-
solving episode). We call this mechanism analogical search control (Jones 1993).
As EUREKA searches through a problem space, it must choose an operator to try next
at each state it reaches. Instead of using a standard match against generalized operators in
memory (which would introduce additional representation requirements), the system finds
analogical situations in memory and maps the operators used there to the new situation.
EUREKA stores only fully instantiated records of its problem-solving experiences in memory.
None of the stored operators contain variables; all operators must be analogically mapped to
new situations. The degree to which they must be mapped depends on the degree of match
between the old and new situations. Thus, operators can map to other problems within the
same domain or across domains, allowing transfer within and across domains to arise from a