This thesis investigates the relationship between language behavior and agents' resource bounds by examining the use of INFORMATIONALLY REDUNDANT UTTERANCES (IRUs) in problem-solving dialogues. The content of an IRU is a proposition that the conversants already know or could infer. Since communication is a subcase of action, the existence of IRUs is a paradox because IRUs appear to be actions whose effects have already been achieved. The explication of the paradox of IRUs has ramifications for models of action in general and of dialogue in particular. I argue that IRUs can only be explained by a processing model of dialogue that reflects agents' autonomy and limited attentional and inferential capacity. The central thesis is that the communicative function of IRUs is related to the cognitive properties of resource-limited agents. In order to investigate this interaction the thesis relies on two empirical methods: (1) distributional analysis of IRUs in a large corpus of naturally occurring dialogues, and (2) dialogue simulations in the Design-World environment which supports the parameterization of the dialogue situation, the task definition, and agents' cognitive properties. The distributional analysis provides support for the claimed communicative functions by showing that IRUs demonstrate agents' autonomy and are used to support deliberation and inference. IRUs help autonomous agents coordinate on a collaborative task given their resource limits. The Design-World simulations show that discourse strategies that include IRUs are beneficial when agents are attention and inference limited or when the task is fault intolerant, inferentially complex, or requires a high degree of agreement. While some types of IRUs are beneficial simply as a rehearsal strategy, the general result is that IRUs are most beneficial when targeted at specific requirements of the communication situation.